Kazuma Morita
For a $p$-adic local field $K$ with perfect residue field, L. Herr constructed a complex which computes the Galois cohomology of a $p$-torsion representation of the absolute Galois group of $K$ by using the theory of $(Φ,Γ)$-modules. We shall generalize his work to the imperfect residue field (the residue field has a finite $p$-basis) case.
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We generalize a work of Iovita-Zaharescu on the Galois theory of B_dR^+ to the imperfect residue field case. The proof is based on a structure theorem of Colmez's higher Kahler differentials.
The $\ell$-adic Galois polylogarithm is an arithmetic function on an absolute Galois group with values in $\ell$-adic numbers, which arises from Galois actions on $\ell$-adic étale paths on ${\mathbb P}^1 \backslash \{0,1,\infty\}$. In the present paper, we discuss a relationship between $\ell$-adic Galois polylogarithms and triple $\ell$-th power residue symbols in some special cases studied by a work of Hirano-Morishita. We show that a functional equation of $\ell$-adic Galois polylogarithms by Nakamura-Wojtkowiak implies a reciprocity law of triple $\ell$-th power residue symbols.
A characterization of ramification groups of local fields with imperfect residue field
该研究借助剩余域完备的局部域的分歧群，刻画了剩余域不完备的局部域的分歧群，并以此重新证明了不同定义下阿贝尔扩张分歧群的一个等式。
In Sen's theory in the imperfect residue field case, Brinon defined a functor from the category of C_p-representations to the category of linear representations of certain Lie algebra. We give a comparison theorem between the continuous Galois cohomology of C_p-representations and the Lie algebra cohomology of the associated representations. The key ingredients of the proof are Hyodo's calculation of Galois cohomology and the effaceability of Lie algebra cohomology for solvable Lie algebras.
Let K be a p-adic local field with residue field k such that [k:k^p]=p^e<\infty and V be a p-adic representation of Gal(\bar{K}/K). Then, by using the theory of p-adic differential modules, we show that V is a potentially crystalline (resp. potentially semi-stable) representation of Gal(\bar{K}/K) if and only if V is a potentially crystalline (resp. potentially semi-stable) representation of Gal(\bar{K^{pf}}/K^{pf}) where K^{pf}/K is a certain p-adic local field whose residue field is the smallest perfect field k^{pf} containing k. As an application, we prove the p-adic monodromy theorem of Fo…
In this paper, we generalise the construction of the Bloch-Kato exponential map to complete discrete valuation fields of mixed characteristic (0,p) whose residue fields have a finite p-basis. As an application we prove an explicit reciprocity law, extending a result of Cherbonnier and Colmez in the classical case. This result relies on the calculation of the Galois cohomology of a p-adic representation V in terms of its (phi,G)-module.
Hasse-Arf property and abelian extensions for local fields with imperfect residue fields
本文在剩余域非完美的完备离散赋值域中，证明了类似完美剩余域情形下全分歧扩张为阿贝尔扩张的条件，并给出Hasse-Arf定理的逆定理，构造了具有非整数上分歧断裂的Galois扩张。
Let $K$ be a mixed characteristic complete discrete valuation field with residue field admitting a finite $p$-basis, and let $G_K$ be the Galois group. We first classify semi-stable representations of $G_K$ by weakly admissible filtered $(φ,N)$-modules with connections. We then construct a fully faithful functor from the category of \emph{integral} semi-stable representations of $G_K$ to the category of Breuil-Kisin $G_K$-modules. Using the integral theory, we classify $p$-divisible groups over the ring of integers of $K$ by minuscule Breuil-Kisin modules with connections.
Crystalline representations and Wach modules in the imperfect residue field case
本文研究了非完美余数域情况下晶格表示与Wach模块的等价关系，并建立了有理Wach模块与晶格表示滤波$φ$-模之间的联系。
Let $K$ be a complete discretely valued field with mixed characteristic $(0, p)$ and imperfect residue field $k_K$. Let $Δ$ be a finite set. We construct an equivalence of categories between finite dimensional $\Bbb{F}_p$-representations of the product of $Δ$ copies of the absolute Galois group of $K$ and multivariable \' etale $(φ, Γ)$-modules over a multivariable Laurent series ring over $k_K$.
On $p$-adic Simpson and Riemann-Hilbert correspondences in the imperfect residue field case
本文在剩余域具有有限p基的混合特征完全离散赋值域上，为Galois群的表示构造p进Simpson与Riemann-Hilbert对应，并由此证明Hodge-Tate与de Rham刚性定理，推广了Morita的结果。
Classically the ramification filtration of the Galois group of a complete discrete valuation field is defined in the case where the residue field is perfect. In this paper, we define without any assumption on the residue field, two ramification filtrations and study some of their properties.
Let $K$ be a complete, discretely valued field with finite residue field and $G_K$ its absolute Galois group. The subject of this note is the study of the set of positive integers $d$ for which there exists an absolutely irreducible $\ell$-adic representation of $G_K$ of dimension $d$ with rational traces on inertia. Our main result is that non-Sophie Germain primes are not in this set when the residue characteristic of $K$ is $> 3$. The result stated in the title is a special case.
The graded quotients of the logarithmic ramification groups of a local field of mixed characteristic is killed by the residue characteristic. Its characters are described by differential forms.
Let $K$ be a complete discrete valuation field of mixed characteristic $(0,p)$ with residue field $k_K$ such that $[k_K:k_K^p]=p^d<\infty$. Let $G_K$ be the absolute Galois group of $K$ and $ρ:G_K\to GL_h(\Q_p)$ a $p$-adic representation. When $k_K$ is perfect, Shankar Sen described the Lie algebra of $ρ(G_K)$ in terms of so-called Sen's operator $Θ$ for $ρ$. When $k_K$ may not be perfect, Olivier Brinon defined $d+1$ operators $Θ_0,...,Θ_d$ for $ρ$, which coincides with Sen's operator $Θ$ in the case of $d=0$. In this paper, we describe the Lie algebra of $ρ(G_K)$ in terms of Brinon's operato…
Geometric properties of homomorphisms between the absolute Galois groups of mixed-characteristic complete discrete valuation fields with perfect residue fields
本文将 Mochizuki 与 Hoshi 关于 $p$-进局部域绝对伽罗瓦群几何同态的判别条件推广到具有完美剩余域的一般混合特征完备离散赋值域，并得到弱 Isom 远阿贝尔结果。
Fekete polynomials associate with each prime number $p$ a polynomial with coefficients $-1$ or $1$ except the constant term, which is 0. These coefficients reflect the distribution of quadratic residues modulo $p$. These polynomials were first considered in the 19th century in relation to the studies of Dirichlet $L$-functions. In our paper, we introduce two closely related polynomials. We then express their special values at several integers in terms of certain class numbers and generalized Bernoulli numbers. Additionally, we study the splitting fields and the Galois group of these polynomial…
We consider the class of complete discretely valued fields such that the residue field is of prime characteristic p and the cardinality of a $p$-base is 1. This class includes two-dimensional local and local-global fields. A new definition of ramification filtration for such fields is given. It appears that a Hasse-Herbrand type functions can be defined with all the usual properties. Therefore, a theory of upper ramification groups, as well as the ramification theory of infinite extensions, can be developed. Next, we consider an equal characteristic two-dimensional local field $K$. We introduc…
Let K be a complete discrete valuation field of mixed characteristic (0,p) and G_K the absolute Galois group of K. In this paper, we will prove the p-adic monodromy theorem for p-adic representations of G_K without any assumption on the residue field of K, for example the finiteness of a p-basis of the residue field of K. The main point of the proof is a construction of (phi,G_K)-module Nrig^+(V) for a de Rham representation V, which is a generalization of Pierre Colmez' Nrig^+(V). In particular, our proof is essentially different from Kazuma Morita's proof in the case when the residue field a…
Let $K$ be a complete discrete valuation field of characteristic zero with residue field $k_K$ of characteristic $p>0$. Let $L/K$ be a finite Galois extension with Galois group $G=\Gal(L/K)$ and suppose that the induced extension of residue fields $k_L/k_K$ is separable. Let $\mathbb{W}_n(\cdot)$ denote the ring of $p$-typical Witt vectors of length $n$. Hesselholt conjectured that the pro-abelian group $\{H^1(G,\mathbb{W}_n(\mathcal{O}_L))\}_{n\geq 1}$ is isomorphic to zero. Hogadi and Pisolkar have recently provided a proof of this conjecture. In this paper, we provide an alternative proof o…
We construct various explicit Herr complexes that compute the Galois cohomology of a $p$-adic representation of the absolute Galois group of a complete discrete valuation field of characteristic $0$ with a perfect residue field of characteristic $p$, using the associated $(φ,τ)$-modules (defined by Xavier Caruso), instead of $(φ,Γ)$-modules. We also give an application to $p$-divisible groups.
Using Felgner's problem I revisit a key issue in using the "Galois Stratification Procedure" that first appeared in [FrS76]. The emphasis here is on using arithmetic homotopy to make the production of Poincare; series attached to general diophantine statements canonical. According to work in progress of Michael Benedikt and E. Hrushovski, Galois stratification - over one finite field - is as efficient as is possible: on a statement of length n, it requires time bounded by a stack of exponentials of length linear in n. This doesn't take advantage of problems prepped for using homotopy aspects, …
The smallest non-abelian p-groups play a fundamental role in the theory of Galois p-extensions. We illustrate this by highlighting their role in the definition of the norm residue map in Galois cohomology. We then determine how often these groups --- as well as other closely related, larger p-groups --- occur as Galois groups over given base fields. We show further how the appearance of some Galois groups forces the appearance of other Galois groups in an interesting way.
Totally ramified subfields of $p$-algebras over discrete valued fields with imperfect residue
本研究针对特征$p$的完备离散赋值域上的$p$-代数，在剩余域$p$-秩满足一定条件下，证明了含全分歧纯不可分极大子域则必含全分歧循环极大子域的猜想，推进了相关代数结构研究。
Faltings extension and Hodge-Tate filtration for abelian varieties over $p$-adic local fields with imperfect residue fields
针对剩余域不完备的特征0p进局部域，定义Z_p上O_K的Faltings扩张，推广Fontaine1981年的构造，为该类域上的阿贝尔簇构建Hodge-Tate滤过。
We study the ramification of fierce cyclic Galois extensions of a local field $K$ of characteristic zero with a one-dimensional residue field of characteristic $p>0$. Using Kato's theory of the refined Swan conductor, we associate to such an extension a ramification datum, consisting of a sequence of pairs $(δ_i,ω_i)$, where $δ_i$ is a positive rational number and $ω_i$ a differential form on the residue field of $K$. Our main result gives necessary and sufficient conditions on such sequences to occur as a ramification datum of a fierce cyclic extension of $K$.
We introduce mod $l$ Milnor invariants of a Galois element associated to Ihara's Galois representation on the pro-$l$ fundamental group of a punctured projective line ($l$ being a prime number), as arithmetic analogues of Milnor invariants of a pure braid. We then show that triple quadratic (resp. cubic) residue symbols of primes in the rational (resp. Eisenstein) number field are expressed by mod $2$ (resp. mod $3$) triple Milnor invariants of Frobenius elements. For this, we introduce dilogarithmic mod $l$ Heisenberg ramified covering ${\cal D}^{(l)}$ of $\mathbb{P}^1$, which may be regarded…
Let $K$ be a complete discrete valued field of characteristic zero with residue field $k_K$ of characteristic $p > 0$. Let $L/K$ be a finite Galois extension with the Galois group $G$ and suppose that the induced extension of residue fields $k_L/k_K$ is separable. In his paper, Hesselholt conjectured that $H^1(G,W(\sO_L))$ is zero, where $\sO_L$ is the ring of integers of $L$ and $W(\sO_L)$ is the Witt ring of $\sO_L$ w.r.t. the prime $p$. He partially proved this conjecture for a large class of extensions. In this paper, we prove Hesselholt's conjecture for all Galois extensions.
Let $K$ be a complete discrete valuation field of mixed characteristic $(0,p)$, whose residue field may not be perfect, and $G_K$ the absolute Galois group of $K$. In the first part of this paper, we prove that Scholl's generalization of fields of norms over $K$ is compatible with Abbes-Saito's ramification theory. In the second part, we construct a functor $\mathbb{N}_{\mathrm{dR}}(V)$ associating a de Rham representation $V$ with a $(φ,\nabla)$-module in the sense of Kedlaya. Finally, we prove a compatibility between Kedlaya's differential Swan conductor of $\mathbb{N}_{\mathrm{dR}}(V)$ and …
Given an elliptic curve $E$ over a local field $K$ with residue characteristic $3$, we investigate the action of the absolute Galois group of $K$ in the case of potentially good reduction. In particular the only not completely known case is that of the $\ell$-adic Galois representation attached to an elliptic curve such that the image of inertia is non-cyclic, and isomorphic to $C_3 \rtimes C_4$. In this work we describe such a representation explicitly.
We study $p$-adic Hodge theory for families of Galois representations over pseudorigid spaces. Such spaces are non-archimedean analytic spaces which may be of mixed characteristic, and which arise naturally in the study of eigenvarieties at the boundary of weight space. We introduce perfect and imperfect overconvergent period rings, and we use the Tate--Sen method to construct overconvergent $(φ, Γ)$-modules for Galois representations over pseudorigid spaces.
We investigate the first two Galois cohomology groups of $p$-extensions over a base field which does not necessarily contain a primitive $p$th root of unity. We use twisted coefficients in a systematic way. We describe field extensions which are classified by certain residue classes modulo $p^n$th powers of a related field, and we obtain transparent proofs and slight generalizations of some classical results of Albert. The potential application to the cyclicity question for division algebras of degree $p$ is outlined.
A Galois scaffold, in a Galois extension of local fields with perfect residue fields, is an adaptation of the normal basis to the valuation of the extension field, and thus can be applied to answer questions of Galois module structure. Here we give a sufficient condition for a Galois scaffold to exist in fully ramified Galois extensions of degree $p^2$ of characteristic $p$ local fields. This condition becomes necessary when we restrict to $p=3$. For extensions $L/K$ of degree $p^2$ that satisfy this condition, we determine the Galois module structure of the ring of integers by finding necessa…
Let r : G_Q -> GL_n Q_l be a motivic l-adic Galois representation. For fixed m > 1 we initiate an investigation of the density of the set of primes p such that the trace of the image of an arithmetic Frobenius at p under r is an m^th power residue modulo p. Based on numerical investigations with modular forms we conjecture (with Ramakrishna) that this density equals 1/m whenever the image of r is open. We further conjecture that for such r the set of these primes p is independent of any set defined by Cebatorev-style Galois theoretic conditions (in an appropriate sense). We then compute these …
Ramification groups of Galois extensions over local fields of positive characteristic with Galois group isomorphic to the group of unitriangular matrices
本文研究特征p>0、完美剩余域的局部域上，伽罗瓦群为UT_n(F_p)的有限伽罗瓦扩张的分歧群，推导上分歧断点的线性表达式，实现无需L-K元素的分歧群计算。
Let K be a complete discrete valuation field of mixed characteristic (0,p) with perfect residue field. Let (π_n)_{n\ge 0} be a system of p-power roots of a uniformizer π=π_0 of K with π^p_{n+1}=π_n, and define G_s (resp.\ G_{\infty}) the absolute Galois group of K(π_s) (resp.\ K_{\infty}:=\bigcup_{n\ge 0} K(π_n)). In this paper, we study G_s-equivatiantness properties of G_{\infty}-equivariant homomorphisms between torsion (potentially) crystalline representations
Let $L/K$ be a finite Galois extension of local fields. The Hasse-Arf theorem says that if Gal$(L/K)$ is abelian then the upper ramification breaks of $L/K$ must be integers. We prove the following converse to the Hasse-Arf theorem: Let $G$ be a nonabelian group which is isomorphic to the Galois group of some totally ramified extension $E/F$ of local fields with residue characteristic $p>2$. Then there is a totally ramified extension of local fields $L/K$ with residue characteristic $p$ such that Gal$(L/K)\cong G$ and $L/K$ has at least one nonintegral upper ramification break.
In this article, we prove that if $H$ is a skew field of center $k$ and $σ$ an automorphism of finite order of $H$ such that the fixed subfield $k^{\langle σ\rangle}$ of $k$ under the action of $σ$ contains an ample field, then the inverse Galois problem has a positive answer over the skew field $H(t,σ)$ of twisted rational fractions. Moreover, if $k^{\langle σ\rangle}$ contains either a real closed field, or an Henselian field of residue characteristic $0$ and containing all roots of unity, then the profree group of countable rank $\widehat{F}_ω$ is a Galois group over $H(t,σ)$.
This text answers a question raised by Joux and the second author about the computation of discrete logarithms in the multiplicative group of finite fields. Given a finite residue field $\bK$, one looks for a smoothness basis for $\bK^*$ that is left invariant by automorphisms of $\bK$. For a broad class of finite fields, we manage to construct models that allow such a smoothness basis. This work aims at accelerating discrete logarithm computations in such fields. We treat the cases of codimension one (the linear sieve) and codimension two (the function field sieve).
Strongly divisible lattices and crystalline cohomology in the imperfect residue field case
本文在不完备剩余域情形下，用强可除格分类半稳定表示的$\mathbf{Z}_p$-格，并给出相关晶体上同调的上同调描述，推广了Liu及Cais-Liu的结果。
In our previous study of duality for complete discrete valuation fields with perfect residue field, we treated coefficients in finite flat group schemes. In this paper, we treat abelian varieties. This in particular implies Grothendieck's conjecture on the perfectness of his pairing between the Neron component groups of an abelian variety and its dual. The point is that our formulation is well-suited with Galois descent. From the known case of semistable abelian varieties, we deduce the perfectness in full generality. We also treat coefficients in tori and, more generally, 1-motives.
We estimate several probability distributions arising from the study of random, monic polynomials of degree $n$ with coefficients in the integers of a general $p$-adic field $K_{\mathfrak{p}}$ having residue field with $q= p^f$ elements. We estimate the distribution of the degrees of irreducible factors of the polynomials, with tight error bounds valid when $q> n^2+n$. We also estimate the distribution of Galois groups of such polynomials, showing that for fixed $n$, almost all Galois groups are cyclic in the limit $q \to \infty$. In particular, we show that the Galois groups are cyclic with p…
Let $F$ be the function field of a curve over a non-archimedean local field. Let $m \geq 2$ be an integer coprime to the characteristic of the residue field of the local field. In this article, we show that every element in $H^{3}(F, μ_{m}^{\otimes 2})$ is of the form $χ\cup (f) \cup (g)$, where $χ$ is in $H^{1}(F, \mathbb{Z}/m\mathbb{Z})$ and $(f)$, $(g)$ in $H^{1}(F, μ_{m})$. This extends a result of Parimala and Suresh, where they show this when $m$ is prime and when $F$ contains $μ_{m}$.
We establish several compatibility results between residue maps in étale and Galois cohomology that arise naturally in the analysis of smooth affine algebraic curves having good reduction over discretely valued fields. These results are needed, and in fact have already been used, for the study of finiteness properties of the unramified cohomology of function fields of affine curves over number fields.
Let $K$ be a complete discrete valuation field of characteristic $(0, p)$ with perfect residue field, and let $T$ be an integral $\mathbb{Z}_p$-representation of $\mathrm{Gal}(\overline{K}/K)$. A theorem of T. Liu says that if $T/p^n T$ is torsion semi-stable (resp. crystalline) of uniformly bounded Hodge-Tate weights for all $n \geq 1$, then $T$ is also semi-stable (resp. crystalline). In this note, we show that we can relax the condition of "uniformly bounded Hodge-Tate weights" to an unbounded (log-)growth condition.
Characterising local fields of positive characteristic by Galois theory and the Brauer group
本文通过绝对伽罗瓦群的小商及Brauer群的p-挠公理，在亏指数至多1的域类中同构刻画了正特征局部域，补充了Efrat-Fesenko的工作。
Let $L/K$ be a finite Galois, totally ramified $p$-extension of complete local fields with perfect residue fields of characteristic $p>0$. In this paper, we give conditions, valid for any Galois $p$-group $G={Gal}(L/K)$ (abelian or not) and for $K$ of either possible characteristic (0 or $p$), that are sufficient for the existence of a Galois scaffold. The existence of a Galois scaffold makes it possible to address questions of integral Galois module structure, which is done in a separate paper. But since our conditions can be difficult to check, we specialize to elementary abelian extensions …
Crystalline part of the Galois cohomology of crystalline representations
针对$p\geqslant3$的非分歧扩张$F/\mathbb{Q}_p$，定义两类带Wach模系数的syntomic复形，证明它们均能计算对应晶体表示的伽罗瓦上同调的晶体部分，还建立了Berger的Wach模到更小周期环的下降性质。
Suppose O is a complete discrete valuation ring of positive characteristic with perfect residue field. The category of finite flat strict modules was introduced recently by Faltings and appears as an equal characteristic analogue of the classical category of finite flat group schemes. In this paper we obtain a classification of these modules and apply it to prove analogues of properties, which were known earlier for group schemes.
Prismatic $F$-crystals and crystalline Galois representations
本文证明了在混合特征完备离散赋值域上，棱晶 $F$-晶体范畴与晶体 $G_K$-表示中的格范畴是等价的。
Let $L/K$ be a Galois extension of number fields with Galois group $G$. We discuss a new method to obtain elements in $\mathbb{Z}[G]$ which annihilate the class group of $L$. Using this method, we obtain annihilators of class groups of cyclotomic fields. We show that these annihilators are new. Some more consequences are also discussed. Moreover, we mention some results and connections to highlight importance of primes of higher residue degree.
Let $(\mathbb{T}_f,\mathfrak{m}_f)$ denote the mod $p$ local Hecke algebra attached to a normalised Hecke eigenform $f$, which is a commutative algebra over some finite field $\mathbb{F}_q$ of characteristic $p$ and with residue field $\mathbb{F}_q$. By a result of Carayol we know that, if the residual Galois representation $\overlineρ_f:G_\mathbb{Q}\rightarrow\mathrm{GL}_2(\mathbb{F}_q)$ is absolutely irreducible, then one can attach to this algebra a Galois representation $ρ_f:G_\mathbb{Q}\rightarrow\mathrm{GL}_2(\mathbb{T}_f)$ that is a lift of $\overlineρ_f$. We will show how one can deter…
Let E be a nonarchimedean local field with residue characteristic l, and suppose we have an n-dimensional representation of the absolute Galois group G_E of E over a reduced complete Noetherian local ring A with finite residue field k of characteristic p different from l. We consider the problem of associating to any such representation an admissible A[GL_n(E)]-module in a manner compatible with the local Langlands correspondence at characteristic zero points of Spec A. In particular we give a set of conditions that uniquely characterise such an A[GL_n(E)]-module if it exists, and show that su…
We prove that the ramification filtration of the absolute Galois group of a comlete discrete valuation field with perfect residue field is characterized in terms of Fontaine's property (Pm).
The distribution of the multiplicative index of algebraic numbers over residue classes
在广义黎曼假设下，研究数域中乘性指数属于指定集合且具有指定弗罗贝尼乌斯元的素理想的自然密度，并重点分析等差数列情形下密度的正性。
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。
Let $L/K$ be a finite, totally ramified $p$-extension of complete local fields with residue fields of characteristic $p > 0$, and let $A$ be a $K$-algebra acting on $L$. We define the concept of an $A$-scaffold on $L$, thereby extending and refining the notion of a Galois scaffold considered in several previous papers, where $L/K$ was Galois and $A=K[G]$ for $G=\mathrm{Gal}(L/K)$. When a suitable $A$-scaffold exists, we show how to answer questions generalizing those of classical integral Galois module theory. We give a necessary and sufficient condition, involving only numerical parameters, f…
Let A be a complete discrete valuation ring with possibly imperfect residue field. The purpose of this paper is to give a notion of conductor for Galois representations over A that generalizes the classical Artin conductor. The definition rests on two general results: there is a moduli space that parametrizes the ways of modifying A so that its residue field is perfect, and any information about a Galois-theoretic object over A can be recovered from its pullback to the (residually perfect) discrete valuation ring corresponding to the generic point of this moduli space.
Let $K$ be a global or local field, $E/K$ a Galois extension, and Br$(E)$ the Brauer group of $E$. This paper shows that if $K$ is a local field, $v$ is its natural discrete valuation, $v'$ is the valuation of $E$ extending $v$, and $q$ is the characteristic of the residue field $\widehat E$ of $(E, v')$, then Br$(E) = \{0\}$ if and only if the following conditions hold: $\widehat E$ contains as a subfield the maximal $p$-extension of $\widehat K$, for each prime $p \neq q$; $\widehat E$ is an algebraically closed field in case the value group $v'(E)$ is $q$-indivisible. When $K$ is a global f…
Galois scaffolds for $p$-extensions in characteristic $p$
本文利用 Saltman 的 generic $G$-扩张构造，在特征 $p$ 的局部域上构造了具有 Galois scaffolds 的全分歧 $G$-扩张，并得到了整数环在关联阶上为秩 1 自由模及关联阶为 Hopf order 的特例。
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