David Burns, Otmar Venjakob
We discuss the formalism of Iwasawa theory descent in the setting of the localized K_1-groups of Fukaya and Kato. We then prove interpolation formulas for the `leading terms' of the global Zeta isomorphisms that are associated to certain Tate motives and of the p-adic L-functions that are associated to certain critical motives.
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We begin a systematic investigation of universal norms for $p$-adic representations in higher rank Iwasawa theory. After establishing the basic properties of the module of higher rank universal norms we construct an Iwasawa-theoretic pairing that is relevant to this setting. This allows us, for example, to refine the classical Iwasawa Main Conjecture for cyclotomic fields, and also to give applications to various well-known conjectures in arithmetic concerning Iwasawa invariants and leading terms of $L$-functions.
Rarity of pseudo-null Iwasawa modules for $p$-adic Lie extensions
该研究得到全实域$p$-进李扩张下$p$-分歧岩泽模伪零性的充要条件，应用于CM域非分歧岩泽模负分量的相关问题，证明这类伪零性十分稀有。
In this article, we discuss Iwasawa Main Conjecture for $p$-adic families of elliptic modular cuspforms. After the overview on the situation of the ordinary case of Hida family, we will introduce a Coleman map for Coleman family for the non-ordinary case (Coleman family) which was obtained as a joint work with Filippo Nuccio [NO16] and we give some results on Iwasawa Theory for Coleman families as applications of . First, we give a construction of a two-variable $p$-adic $L$-function for a Coleman family thanks to the ingredients given in [NO16] (Theorem 5.1). Combining this result and Coleman…
We prove under mild hypotheses the three-variable Iwasawa main conjecture for $p$-ordinary modular forms in the indefinite setting. Our result is in a setting complementary to that in the work of Skinner-Urban, and it has applications to Greenberg's nonvanishing conjecture for the first derivatives at the center of $p$-adic $L$-functions of cusp forms in Hida families with root number $-1$ and to Howard's horizontal nonvanishing conjecture.
Noncommutative Iwasawa theory has created a lot of interest in Whitehead groups of Iwasawa algebras of compact p-adic Lie groups with a quotient isomorphic to the additive group of p-adic integers. In this paper we compute Whitehead groups of Iwasawa algebra of a pro-p compact p-adic Lie group of dimension one. We also give results on Whitehead groups of the localisation of such Iwasawa algebras at the canonical Ore set defined by Coates, Fukaya, Kato, Sujatha and Venjakob.
We describe an explicit `higher rank' Iwasawa theory for zeta elements associated to the multiplicative group over abelian extensions of general number fields. We then show that this theory leads to a concrete new strategy for proving special cases of the equivariant Tamagawa number conjecture. As a first application of this approach, we use it to prove new cases of the conjecture for Tate motives over natural families of abelian CM extensions of totally real fields for which the relevant $p$-adic $L$-functions possess trivial zeroes.
In this paper the new techniques and results concerning the structure theory of modules over non-commutative Iwasawa algebras are applied to arithmetic: we study Iwasawa modules over p-adic Lie extensions K of number fields k "up to pseudo-isomorphism". In particular, a close relationship is revealed between the Selmer group of abelian varieties, the Galois group of the maximal abelian unramified p-extension of K as well as the Galois group of the maximal abelian outside S unramified p-extension where S is a finite set of certain places of k. Moreover, we determine the Galois module structure …
We construct an Euler system of $p$-adic zeta elements over the eigencurve which interpolates Kato's zeta elements over all classical points. Applying a big regulator map gives rise to a purely algebraic construction of a two-variable $p$-adic $L$-function over the eigencurve. As a first application of these ideas, we prove the equality of the $p$-adic $L$-functions associated with a critical-slope refinement of a modular form by the works of Bellaïche/Pollack-Stevens and Kato/Perrin-Riou.
In this paper we prove that the $p$-adic $L$-function that interpolates the Rankin-Selberg product of a general weight two modular form which is unramified and non-ordinary at $p$, and an ordinary CM form of higher weight contains the characteristic ideal of the corresponding Selmer group. This is one divisibility of the Iwasawa-Greenberg main conjecture for the $p$-adic $L$-function. This generalizes an earlier work of the author to the non-ordinary case. The result of this paper plays a crucial role in the proof of Iwasawa main conjecture and refined Birch-Swinnerton-Dyer formula for supersi…
We recover a result of Iwasawa on the p-adic logarithm of principal units with the use of the value at 1 of p-adic L-functions. We deduce an Iwasawa-like result in the odd part of principal units.
On the Iwasawa invariants of Kato's zeta elements for modular forms
研究Kato主猜想中不依赖p-进L函数的Iwasawa模的不变量行为，推广Greenberg-Vatsal等人的工作，并在Katoζ元素模p非零的假设下建立高权重模形式的主猜想传播。
We revisit the theory of Ihara $L$-functions in the context initially studied by Bass and Hashimoto and more recently by Zakharov. In particular, we study if the Artin formalism is satisfied by these $L$-functions. As an application, we give a proof of the analogue of Iwasawa's asymptotic class number formula for the $p$-part of the number of spanning trees in branched $\mathbb{Z}_{p}$-towers of finite connected graphs using Ihara zeta and $L$-functions. Moreover, we relate a generator for the characteristic ideal of the finitely generated torsion Iwasawa module that governs the growth of the …
In this paper we prove that the p-adic L-function that interpolates the Rankin-Selberg product of a general modular form and a CM form of higher weight divides the characteristic ideal of the corresponding Selmer group. This is one divisibility of the Iwasawa main conjecture for the p-adic L-function. We prove this conjecture using the congruences between Klingen Eisensteinseries and cusp forms on the group GU(3; 1), following the strategy of a recent work of C. Skinner and E. Urban. This theorem can be used to deduce a converse of Gross-Zagier-Kolyvagin theorem and the precise BSD formula in …
A result due to R. Greenberg gives a relation between the cardinality of Selmer groups of elliptic curves over number fields and the characteristic power series of Pontryagin duals of Selmer groups over cyclotomic $\mathbb Z_p$-extensions at good ordinary primes $p$. We extend Greenberg's result to more general $p$-adic Galois representations, including a large subclass of those attached to $p$-ordinary modular forms of level $Γ_0(N)$ with $p\nmid N$.
This paper is lead by the question whether there is a nice structure theory of finitely generated modules over the Iwasawa algebra, i.e. the completed group algebra, R of a p-adic analytic group G. For G without any p-torsion element we prove that R is an Auslander regular ring. This result enables us to give a good definition for pseudo-null R-modules. Then the category of R-modules up to pseudo-isomorphisms is studied and we obtain a weak structure theorem for the p-primary part of a finitely generated R-module. A local duality theorem as well as the Auslander-Buchsbaum equality are further …
We prove Mazur and Rubin's Iwasawa-theoretic Gross-Zagier conjecture (under some restrictive hypotheses), which relates Heegner points in towers of number fields to the 2-variable p-adic L-function. The result generalizes Perrin-Riou's p-adic Gross-Zagier theorem.
In this paper, we define a two-variable analogue of Perrin-Riou's p-adic regulator map for the Iwasawa cohomology of a crystalline representation of the absolute Galois group of $\mathbf{Q}_p$, over a Galois extension of $\mathbf{Q}_p$ whose Galois group is an abelian p-adic Lie group of dimension 2. We use this regulator map to study p-adic representations of global Galois groups over certain abelian extensions of number fields whose localisation at the primes above p are extensions of the above type. In the example of the restriction to an imaginary quadratic field of the representation atta…
Let $p$ be a prime number, and $G$ a compact $p$-adic Lie group. We recall that the Iwasawa algebra $Λ(G)$ is defined to be the completed group ring of $G$ over the ring of $p$-adic integers. Interesting examples of finitely generated modules over $Λ(G),$ in which $G$ is the image of Galois in the automorphism group of a $p$-adic Galois representation, abound in arithmetic geometry. The study of such $Λ(G)$-modules arising from arithmetic geometry can be thought of as a natural generalization of Iwasawa theory. One of the cornerstones of classical Iwasawa theory is the fact that, when $G$ is t…
This article is the first of a pair of articles dealing with the Iwasawa theory of modular forms of weight 1 and, more generally, of Artin representations satisfying certain conditions. The main results in this part analyze the structure of certain Selmer groups for the Artin representation. In particular, it is shown that the Selmer groups are co-torsion as $Λ$-modules. For each Selmer group, we consider a generator of the characteristic ideal of its Pontrjagin dual. We call that the algebraic p-adic L-function. We also construct an analytic $p$-adic L-function via deformation to higher weigh…
Iwasawa invariants of sharp/flat $2$-adic $L$-functions for quadratic twists of elliptic curves
研究\(\mathbb{Q}\)上在\(2\)处具有良好超奇异约化的椭圆曲线的Sprung尖点/平坦2 - 进\(L\)函数解析岩泽不变量在二次扭转下的变化，\(\mu\) - 不变量为零时给出\(\lambda\) - 不变量的显式差分公式及应用。
This article extends our study of the geometry of the $p$-adic eigencurve at a point defined by a weight $1$ cuspform $f$ irregular at $p$ and having complex multiplication, and the implications in Iwasawa and in Hida theories. The novel results include the determination of the Fourier coefficients of certain non-classical $p$-adic modular forms belonging to the generalized eigenspace of $f$, in terms of $p$-adic logarithms of algebraic numbers. We also compute the "mysterious" cross-ratios of the $p$-ordinary filtrations of the Hida families containing $f$.
In 2005 Coates, Fukaya, Kato, Sujatha, and Venjakob formulated a noncommutative Iwasawa main conjecture for l-adic Lie extensions of number fields. To provide evidence for this main conjecture we formulate and prove an analogous statement for l-adic Lie extensions of separated schemes of finite type over a finite field of characteristic prime to l.
Iwasawa made the fundamental discovery that there is a close connection between the ideal class groups of $\mathbb{Z}_{p}$-extensions of cyclotomic fields and the $p$-adic analogue of Riemann's zeta functions $$ζ(s)=\sum_{n=1}^{\infty}\frac{1}{n^{s}}.$$ In this paper, we show that there may also exist a parallel Iwasawa's theory corresponding to the $p$-adic analogue of Euler's deformation of zeta functions $$ϕ(s)=\sum_{n=1}^{\infty}\frac{(-1)^{n-1}}{n^{s}}.$$
In this article we construct characteristic elements for a certain class of Iwasawa modules in noncommutative Iwasawa theory. These elements live in the first K-group K_1(L_T) of the localisation L_T of the Iwasawa algebra L=L(G) of a p-adic Lie group G with respect to a certain Ore-Set T. The evaluation of the characteristic element of a module M under the Iwasawa algebra of the p-adic Lie group G is related to the (twisted) G-Euler characteristic of M. We apply these results to study the arithmetic of elliptic curves E (without CM) defined over a number field k in the tower K=k(E(p)) of fiel…
The paper starts out from pseudomeasures (in the sense of Serre) which hold the arithmetic properties of the abelian $l$-adic Artin $L$-functions over totally real number fields. In order to generalize to non-abelian $l$-adic $L$-functions, these abelian pseudomeasures must satisfy congruences which are introduced but not yet known to be true. The relation to the ``equivariant main conjecture'' of Iwasawa theory is discussed.
A result of Bleher, Chinburg, Greenberg, Kakde, Pappas, Sharifi and Taylor has initiated the topic of higher codimension Iwasawa theory. As a generalization of the classical Iwasawa main conjecture, they prove a relationship between analytic objects (a pair of Katz's $2$-variable $p$-adic $L$-functions) and algebraic objects (two "everywhere unramified'' Iwasawa modules) involving codimension two cycles in a $2$-variable Iwasawa algebra. We prove a result by considering the restriction to an imaginary quadratic field $K$ (where an odd prime $p$ splits) of an elliptic curve $E$, defined over $\…
On generalized Iwasawa main conjectures and $p$-adic Stark conjectures for Artin motives
本文提出关于Artin动机的广义Iwasawa主猜想和$p$-adic Stark猜想，并证明其与Rubin-Stark元素的等价性及虚二次域中相关猜想的无条件成立。
Fix an odd prime $p$. Let $G$ be a compact $p$-adic Lie group containing a closed, normal, pro-$p$ subgroup $H$ which is abelian and such that $G/H$ is isomorphic to the additive group of $p$-adic integers $\mathbbZ_p$ . First we assume that $H$ is finite and compute the Whitehead group of the Iwasawa algebra, $Λ(G)$, of $G$. We also prove some results about certain localisation of $Λ(G)$ needed in Iwasawa theory. Let $F$ be a totally real number field and let $F_{\infty}$ be an admissible $p$-adic Lie extension of $F$ with Galois group $G$. The computation of the Whitehead groups are used to …
On the Iwasawa invariants of BDP Selmer groups and BDP P-adic L-fucntions
本文将分圆情形下权2赫克本征尖点形式的p准素塞尔默群与p进L函数的岩泽不变量关系，推广到反分圆情形，研究虚二次域下满足广义Heegner假设的两个形式的BDP塞尔默群与BDP p进L函数的岩泽不变量关联。
We discuss the triviality of some classical Iwasawa modules in connection with the notion of $\ell$-rationality for totally $\ell$-adic number fields.
Iwasawa algebras of compact $p$-adic Lie groups are completed group algebras with applications in number theory in studying class numbers of towers of number fields and representation theory of $p$-adic Lie groups. In our earlier work, we determined an explicit presentation of the Iwasawa algebra for the first principal congruence kernel of Chevalley groups over $\mathbb{Z}_p$. In this paper, for prime $p>n+1$, we extend our result to determine the explicit presentation, in the form of generators and relations, of the Iwasawa algebra of the pro-$p$ Iwahori subgroup of $GL_n(\mathbb{Z}_p)$.
The central result of this paper is a refinement of Hida's duality theorem between ordinary Lambda-adic modular forms and the universal ordinary Hecke algebra. Specifically, we give a necessary condition for this duality to be integral with respect to particular submodules of the space ordinary Lambda-adic modular forms. This refinement allows us to give a simple proof that the universal ordinary cuspidal Hecke algebra modulo Eisenstein ideal is isomorphic to the Iwasawa algebra modulo an ideal related to the Kubota-Leopoldt p-adic L-function. The motivation behind these results stems from Oht…
The purpose of this paper is to build on results in {\it{higher codimension Iwasawa theory}}. The setting of our results involves Galois representations arising as cyclotomic twist deformations associated to (i) the tensor product of two cuspidal Hida families $F$ and $G$, and (ii) the tensor product of three cuspidal Hida families $F$, $G$ and $H$. On the analytic side, we consider (i) a pair of $3$-variable Rankin-Selberg $p$-adic $L$-functions constructed by Hida and (ii) a balanced $4$-variable $p$-adic $L$-function (due to Hsieh and Yamana) and an unbalanced $4$-variable $p$-adic $L$-func…
An introduction to $p$-adic $L$-functions
本文以三种等价方式介绍p进L-函数与Iwasawa理论，并陈述Iwasawa主猜想及Vandiver素数情形下的证明。
Special values of $p$-adic $L$-functions and Iwasawa $λ$-invariants of Dirichlet characters
本文研究奇素数p对应的狄利克雷特征χ的岩泽λ不变量，利用p进L函数特殊值推导λ取值判据，扩展相关方法计算λ不变量，并生成其分布数值数据。
Let f be a cuspidal newform with complex multiplication (CM) and let p be an odd prime at which f is non-ordinary. We construct admissible p-adic L-functions for the symmetric powers of f, thus verifying general conjectures of Dabrowski and Panchishkin in this special case. We also construct their "mixed" plus and minus counterparts and prove an analogue of Pollack's decomposition of the admissible p-adic L-functions into mixed plus and minus p-adic L-functions. On the arithmetic side, we define corresponding mixed plus and minus Selmer groups. We unite the arithmetic with the analytic by firs…
In the present paper, we study the $p$-adic $L$-functions and the (strict) Selmer groups over $\mathbb{Q}_{\infty}$, the cyclotomic $\mathbb{Z}_p$-extension of $\mathbb{Q}$, of the $p$-adic weight one cusp forms $f$, obtained via the $p$-stabilization of weight one Eisenstein series, under the assumption that a certain Eisenstein component of the $p$-ordinary universal cuspidal Hecke algebra is Gorenstein. As an application, we compute the Iwasawa invariants of ordinary modular forms of weight $k\geq 2$ with the same residual Galois representations as the one of $f$, which in our setting, is r…
This paper pursues positive characteristic analogues of the results of Furusho, Komori, Matsumoto and Tsumura on $p$-adic multiple $L$-functions. We consider $\infty$-adic and $v$-adic multiple zeta functions concerned by Anglès, Ngo Dac and Tavares Ribeiro. Our main results in this paper consist of: (1) integral expressions of special values of $\infty$-adic multiple zeta functions, (2) integral expression of $v$-adic multiple zeta functions themselves similar to those of $p$-adic multiple $L$-functions, (3) Kummer-type congruence for the special values of $v$-adic multiple zeta functions at …
In a previous paper we constructed a new class of Iwasawa modules as $\ell$--adic realizations of what we called abstract $\ell$--adic $1$--motives in the number field setting. We proved in loc. cit. that the new Iwasawa modules satisfy an equivariant main conjecture. In this paper we link the new modules to the $\ell$--adified Tate canonical class, defined by Tate in 1960 and give an explicit construction of (the minus part of) $\ell$--adic Tate sequences for any Galois CM extension $K/k$ of an arbitrary totally real number field $k$. These explicit constructions are significant and useful in…
We establish the Iwasawa main conjecture for semi-stable abelian varieties over a function field of characteristic $p$ under certain restrictive assumptions. Namely we consider $p$-torsion free $p$-adic Lie extensions of the base field which contain the constant $\mathbb Z_p$-extension and are everywhere unramified. Under the classical $μ=0$ hypothesis we give a proof which mainly relies on the interpretation of the Selmer complex in terms of $p$-adic cohomology [TV] together with the trace formulas of [EL1].
We give a survey of a couple known constructions of $p$-adic $L$-functions including Iwasawa's construction from classical Stickelberger elements. We then construct "real" Stickelberger elements, i.e., explicit elements in the Galois group ring with $\mathbb{Z}_p$ coefficients that annihilate the Sylow $p$-subgroup of the ideal class group of $\mathbb{Q}(ζ_{p^{n+1}})^+$. In analogy with Iwasawa's work, we show that these elements are coherent in $\mathbb{Z}_p$-towers and give rise to twisted $p$-adic $L$-functions.
On the Iwasawa Main Conjecture for generalized Heegner classes in a quaternionic setting
本文针对更高权普通模形式与满足松弛Heegner假设的虚二次域，沿用Howard等的方法构造广义Heegner类的$Λ$-进Kolyvagin系统，证明了反循环岩泽主猜想的一个整除关系，并将其应用于Magrone定义的$p$-进$L$-函数的岩泽-格林伯格主猜想。
We extend Kobayashi's formulation of Iwasawa theory for elliptic curves at supersingular primes to include the case $a_p \neq 0$, where $a_p$ is the trace of Frobenius. To do this, we algebraically construct $p$-adic $L$-functions $L_p^{\sharp}$ and $L_p^{\flat}$ with the good growth properties of the classical Pollack $p$-adic $L$-functions that in fact match them exactly when $a_p=0$ and $p$ is odd. We then generalize Kobayashi's methods to define two Selmer groups $\Sel^{\sharp}$ and $\Sel^{\flat}$ and formulate a main conjecture, stating that each characteristic ideal of the duals of these…
Fine Selmer groups of modular forms
研究模形式的细Selmer群与理想类群的Iwasawa不变量，比较其秩和μ不变量。
This work is a study of $p$-adic multiple zeta values at roots of unity ($p$MZV$μ_{N}$'s), the $p$-adic periods of the crystalline pro-unipotent fundamental groupoid of $(\mathbb{P}^{1} - \{0,μ_{N},\infty\})/ \mathbb{F}_{q}$. The main tool is new objects which we call $p$-adic pro-unipotent harmonic actions. In this part IV we define and study $p$-adic analogues of some elementary complex analytic functions which interpolate multiple zeta values at roots of unity such as the multiple zeta functions. The indices of $p$MZV$μ_{N}$'s involve sequences of positive integers ; in this IV-1, by consid…
We prove that the algebra of p-adic multi-zeta values are contained in another algebra which is defined explicitly in terms of series.
Let $L/K$ be a finite Galois extension of $p$-adic fields and let $L_{\infty}$ be the unramified $\mathbb Z_p$-extension of $L$. Then $L_{\infty}/K$ is a one-dimensional $p$-adic Lie extension. In the spirit of the main conjectures of equivariant Iwasawa theory, we formulate a conjecture which relates the equivariant local epsilon constants attached to the finite Galois intermediate extensions $M/K$ of $L_{\infty}/K$ to a natural arithmetic invariant arising from the étale cohomology of the constant sheaf $\mathbb Q_p/\mathbb Z_p$ on the spectrum of $L_{\infty}$. We give strong evidence of the…
We consider the family of CM-fields which are pro-p p-adic Lie extensions of number fields of dimension at least two, which contain the cyclotomic Z_p-extension, and which are ramified at only finitely many primes. We show that the Galois groups of the maximal unramified abelian pro-p extensions of these fields are not always pseudo-null as Iwasawa modules for the Iwasawa algebras of the given p-adic Lie groups. The proof uses Kida's formula for the growth of lambda-invariants in cyclotomic Z_p-extensions of CM-fields. In fact, we give a new proof of Kida's formula which includes a slight weak…
We study a refinement of the symmetric multiple zeta value, called the $t$-adic symmetric multiple zeta value, by considering its finite truncation. More precisely, two kinds of regularizations (harmonic and shuffle) give two kinds of the $t$-adic symmetric multiple zeta values, thus we introduce two kinds of truncations correspondingly. Then we show that our truncations tend to the corresponding $t$-adic symmetric multiple zeta values, and satisfy the harmonic and shuffle relations, respectively. This gives a new proof of the double shuffle relations for $t$-adic symmetric multiple zeta value…
We compute the Archimedean doubling zeta integrals which appear in the interpolation formulas for the p-adic L-functions of Siegel modular forms, and verify that they agree with the modified Archimedean Euler factors for p-adic interpolation conjectured by Coates--Perrin-Riou.
The higher rank Lefschetz formula for p-adic groups is used to prove rationality of a several-variable zeta function attached to the action of a p-adic group on its Bruhat-Tits building. By specializing to certain lines one gets one-variable zeta functions, which then can be related to geometrically defined zeta functions
The fact that the double zeta values at n and m can be written as a sum of products of two zeta values and of zeta value at m+n, whenever n+m is odd is due to Euler. We shall show a weak version of this result for the Galois l-adic realization.
The article is dedicated to the memory of George Voronoi. It is concerned with ($p$-adic) $L$-functions (in partially ($p$-adic) zeta functions) and cyclotomic ($p$-adic) (multiple) zeta values. The beginning of the article contains a short summary of the results on the Bernoulli numbers associated with the studies of George Voronoi. Results on multiple zeta values have presented by D. Zagier, by P. Deligne and A.Goncharov, by A. Goncharov, by F. Brown, by C. Glanois and others. S. Ünver have investigated p-adic multiple zeta values in the depth two. Tannakian interpretation of p-adic multiple…
Inspired by Warren Sinnott 's method we prove a linear independence result modulo p for the Iwasawa power series associated to Kubota-Leopoldt p-adic L-functions.
In this paper we develop a new method to study Iwasawa theory and Eisenstein families for unitary groups $\mathrm{U}(r,s)$ of general signature over a totally real field $F$. As a consequence we prove that for a motive corresponding to a regular algebraic cuspidal automorphic representation $π$ on $\mathrm{U}(r,s)_{/F}$ which is ordinary at $p$, twisted by a Hecke character, if its Selmer group has rank $0$, then the corresponding central $L$-value is nonzero. This generalizes a result of Skinner-Urban in their ICM 2006 report in the special case when $F=\mathbb{Q}$ and the motive is conjugate…
In this short note, we give a proof of the Riemann hypothesis for Goss $v$-adic zeta function $ζ_{v}(s)$, when $v$ is a prime of $\mathbb{F}_{q}[t]$ of degree one.
For a crystalline p-adic representation of the absolute Galois group of Qp, we define a family of Coleman maps (linear maps from the Iwasawa cohomology of the representation to the Iwasawa algebra), using the theory of Wach modules. Let f = sum(a_n q^n) be a normalized new modular eigenform and p an odd prime at which f is either good ordinary or supersingular. By applying our theory to the p-adic representation associated to f, we define two Coleman maps with values in the Iwasawa algebra of Zp^* (after extending scalars to some extension of Qp). Applying these maps to the Kato zeta elements …
Let f be a CM modular form and p an odd prime which is inert in the CM field. We construct two p-adic L-functions for the symmetric square of f, one of which has the same interpolating properties as the one constructed by Delbourgo-Dabrowski, whereas the second one has a similar interpolating properties but corresponds to a different eigenvalue of the Frobenius. The symmetry between these two p-adic L-functions allows us to define the plus and minus p-adic L-functions à la Pollack. We also define the plus and minus p-Selmer groups analogous to Kobayashi's Selmer groups. We explain how to relat…
Anticyclotomic Iwasawa theory of CM elliptic curves at ramified primes
该研究针对CM域中分歧素数处的CM椭圆曲线，构建反分圆岩泽理论的整框架，定义带符号塞尔默群，证明相关岩泽主猜想，填补了无非三角几何形变的对应理论空白。
On a lifting of $t$-adic symmetric multiple zeta values
本文提出带新参数 $s$ 的 $(s,t)$-进对称多重 zeta 值，建立其双重洗牌关系、对偶性与循环和公式，并讨论有限对应物。
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