Antonio Lei
Given an elliptic curve with supersingular reduction at an odd prime p, Iovita and Pollack have generalised results of Kobayashi to define even and odd Coleman maps at p over Lubin-Tate extensions given by a formal group of height 1. We generalise this construction to modular forms of higher weights.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
继续探索
Eigenspaces of Coleman's Trace Operator
本文探讨推广 Coleman 幂级数使其关于两种 Lubin-Tate 形式群律相容的问题，通过精确表述并利用 Coleman 迹算子的特征空间给出了部分分类解答。
Twisted Lubin-Tate Big Witt Vectors and Fleck-Sun-Wan Congruences
本文构造了与扭曲 Lubin-Tate 形式群相关的大 Witt 理论，引入 Fleck 算子并证明了 Fleck-Sun-Wan 同余式的 Lubin-Tate 类比，推广了现有 Witt 理论。
We show that the conjectural mod $p$ local Langlands correspondence can be realised in the mod $p$ cohomology of the Lubin-Tate towers. The proof utilizes a well known conjecture of Buzzard-Diamond-Jarvis \cite[Conj. 4.9]{BDJ10}, a study of completed cohomology of the ordinary and supersingular locus of the Shimura curves for a totally real field $F$ and of mod $l(\neq p)$ local Langlands correspondence as given by Emerton-Helm \cite{EmertonHelm14}. %And then we connect the completed cohomlgy with the cohomology of Lubin-Tate towers. In the case of modular curves a similar theorem was obtained…
In my 2009 paper at Inventiones, we determine the cohomology of Lubin-Tate spaces globally using the comparison theorem of Berkovich by computing the fibers at supersingular points of the perverse sheaf of vanishing cycle $Ψ$ of some Shimura variety of Kottwitz-Harris-Taylor type. The most difficult argument deals with the control of maps of the spectral sequences computing the sheaf cohomology of both Harris-Taylor perverse sheaves and those of $Ψ$. In this paper, we bypass these difficulties using the classical theory of representations of the mirabolic group and a simple geometric argument.
We analyse the mod p étale cohomology of the Lubin-Tate tower both with compact support and without support. We prove that there are no supersingular representations in the H^1_c of the Lubin-Tate tower. On the other hand, we show that in H^1 of the Lubin-Tate tower appears the mod p local Langlands correspondence and the mod p local Jacquet-Langlands correspondence, which we define in the text. We discuss the local-global compatibility part of the Buzzard-Diamond-Jarvis conjecture which appears naturally in this context.
We generalise works of Kobayashi to give a formulation of the Iwasawa main conjecture for modular forms at supersingular primes. In particular, we give analogous definitions of even and odd Coleman maps for normalised new forms of arbitrary weights and relate Pollack's $p$-adic $L$-functions to the even and odd Selmer groups. In addition, by generalising works of Pollack and Rubin on CM elliptic curves, we prove the "main conjecture" for CM modular forms.
We produce an integral model for the modular curve $X(Np^m)$ over the ring of integers of a sufficiently ramified extension of $\mathbf{Z}_p$ whose special fiber is a {\em semistable curve} in the sense that its only singularities are normal crossings. This is done by constructing a semistable covering (in the sense of Coleman) of the supersingular part of $X(Np^m)$, which is a union of copies of a Lubin-Tate curve. In doing so we tie together nonabelian Lubin-Tate theory to the representation-theoretic point of view afforded by Bushnell-Kutzko types. For our analysis it was essential to work …
Let K be a finite extension of Q_p with residue field F_q and let P(T) = T^d + a_{d-1}T^{d-1} + ... +a_1 T, where d is a power of q and a_i is in the maximal ideal of K for all i. Let u_0 be a uniformizer of O_K and let {u_n}_{n \geq 0} be a sequence of elements of Q_p^alg such that P(u_{n+1}) = u_n for all n \geq 0. Let K_infty be the field generated over K by all the u_n. If K_infty / K is a Galois extension, then it is abelian, and our main result is that it is generated by the torsion points of a relative Lubin-Tate group (a generalization of the usual Lubin-Tate groups). The proof of this…
We give a new proof of the properness of the Coleman-Mazur eigencurve. The question of whether the eigencurve satisfies the valuative criterion for properness was first asked by Coleman and Mazur in 1998 and settled by Diao and Liu in 2016 using deep, powerful Hodge- and Galois- theoretic machinery. Our proof is short and explicit and uses no Galois theory. Instead we adapt an earlier method of Buzzard and Calegari based on elementary properties of overconvergent modular forms. To facilitate this, we extend Pilloni's geometric construction of overconvergent forms of arbitrary weight farther in…
Parametrization of Formal Norm Compatible Sequences
本文分类了参数化Lubin-Tate迹兼容序列的幂级数，回答了Berger和Fourquaux的问题，推广了Coleman的插值定理，并与Kolyvagin合作给出了特殊情形下显式构造方法。
We study the good reduction modulo p of K3 surfaces with complex multiplication. If a K3 surface with complex multiplication has good reduction, we calculate the Picard number and the height of the formal Brauer group of the reduction. Moreover, if the reduction is supersingular, we calculate its Artin invariant under some assumptions. Our results generalize some results of Shimada for K3 surfaces with Picard number 20. Our methods rely on the main theorem of complex multiplication for K3 surfaces by Rizov, an explicit description of the Breuil-Kisin modules associated with Lubin-Tate characte…
For the $p$-cyclotomic tower of $\mathbb{Q}_p$ Fontaine established a description of local Iwasawa cohomology with coefficients in a local Galois representation $V$ in terms of the $ψ$-operator acting on the attached etale $(φ,Γ)$-module $D(V)$. In this article we generalize Fontaine's result to the case of arbitratry Lubin-Tate towers $L_\infty$ over finite extensions $L$ of $\mathbb{Q}_p$ by using the Kisin-Ren/Fontaine equivalence of categories between Galois representations and $(φ_L,Γ_L)$-module and extending parts of [Herr L.: Sur la cohomologie galoisienne des corps $p$-adiques. Bull. S…
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 …
On the growth of Tate-Shafarevich groups of $p$-supersingular abelian varieties of ${\rm GL}_2$-type over $\mathbb{Z}_p$-extensions of number fields
研究具有实乘法的GL2型p-超奇异阿贝尔簇在数域Zp扩张上的Mordell-Weil秩有界性及Tate-Shafarevich群v-primary部分增长，构造局部点系与带符号Coleman映射，证明秩有界并给出渐近公式，推广了椭圆曲线情形。
We prove a $p$-converse theorem for elliptic curves $E/\mathbb{Q}$ with complex multiplication by the ring of integers $\mathcal{O}_K$ of an imaginary quadratic field $K$ in which $p$ is ramified. Namely, letting $r_p = \mathrm{corank}_{\mathbb{Z}_p}\mathrm{Sel}_{p^{\infty}}(E/\mathbb{Q})$, we show that $r_p \le 1 \implies \mathrm{rank}_{\mathbb{Z}}E(\mathbb{Q}) = \mathrm{ord}_{s = 1}L(E/\mathbb{Q},s) = r_p$ and $\#\mathrm{Sha}(E/\mathbb{Q}) < \infty$. In particular, this has applications to two classical Diophantine problems. First, it resolves Sylvester's conjecture on rational sums of cubes…
We discuss abelian equivariant Iwasawa theory for elliptic curves over $\mathbb{Q}$ at good supersingular primes and non-anomalous good ordinary primes. Using Kobayashi's method, we construct equivariant Coleman maps, which send the Beilinson-Kato element to the equivariant $p$-adic $L$-functions. Then we propose equivariant main conjectures and, under certain assumptions, prove one divisibility via Euler system machinery. As an application, we prove a case of a conjecture of Mazur-Tate.
Lubin-Tate moduli space of semisimple mod p Galois representations for GL_2 and Hecke modules
本文为 GL_2 定义了半单模 p Galois 表示的 Lubin-Tate 模空间，并构造了从 pro-p-Iwahori-Hecke 代数中心到该空间的态射，在 F/Q_p 情形下证明了其与 Grosse-Klönne 双射一致。
On the factorisation of the $p$-adic Rankin-Selberg $L$-function in the supersingular case
本文研究了超奇异情况下 $p$-adic Rankin-Selberg $L$-函数的因子分解，通过构造双变量解析 $p$-adic $L$-函数，证明了其与对称平方 $L$-函数和 Kubota-Leopoldt $L$-函数的乘积关系。
We compute the stable reduction of the Lubin-Tate space $X(π^2)$ in the equal characteristic case, on the basis of Coleman-McMurdy's ideas. Namely, in this paper, we actually construct a stable covering of $X(π^2).$ This paper also includes intersection multiplicity datum of the stable model of $X(π^2)$. Our method is very explicit and elementary.
In this paper, we study the Iwasawa theory of a motive whose Hodge-Tate weights are $0$ or $1$ (thence in practice, of a motive associated to an abelian variety) at a non-ordinary prime, over the cyclotomic tower of a number field that is either totally real or CM. In particular, under certain technical assumptions, we construct Sprung-type Coleman maps on the local Iwasawa cohomology groups and use them to define integral $p$-adic $L$-functions and (one unconditionally and other conjecturally) cotorsion Selmer groups. This allows us to reformulate Perrin-Riou's main conjecture in terms of the…
From Orientations to $\ell$-adic Period Vectors
本文提出连接定向超奇异椭圆曲线与模曲线算术的桥梁，通过Coleman积分计算ℓ-adic周期向量，并探讨模符号逆问题及其在密码学中的应用。
We construct an integral model for Lubin-Tate curves as moduli of finite subgroups of formal deformations over complete Noetherian local rings. They are p-adic completions of the modular curves X_0(p) at a mod-p supersingular point. Our model is semistable in the sense that the only singularities of its special fiber are normal crossings. Given this model, we obtain a uniform presentation for the Dyer-Lashof algebra of Morava E-theories at height 2 as local moduli of power operations in elliptic cohomology.
Let $p$ be a prime number such that the modular curve $X_0(p)$ has genus at least two. We show that the only points of the reduction mod $p$ of $X_0(p)$ with image in the reduction mod $p$ of $J_0(p)$ in the cuspidal group are the two cusps. This answers a question of Robert Coleman. For the proof we give a description of the special fibre of the Néron model of the jacobian of a semi-stable curve in terms of divisors. We also study to what extent the morphism from a semistable curve with given base point to the Néron model of its jacobian is a closed immmersion. Implicitly, logarithmic structu…
Fields of definition of $p$-torsion points of elliptic curves and their ramification
研究椭圆曲线p-挠点生成域及其分歧，确定好约化下各点定义域及坏约化下最大上分歧跳跃，并给出数域上无p挠的全局应用。
扫码添加微信好友，提出您的宝贵建议 👇
💡 备注请填写：网站反馈
发表机构由 AI 从论文文本抽取，如发现错误，欢迎反馈修正建议。