Related papers: On Perrin-Riou's exponential map for $(\varphi, \G…

The aim of this article is to study Bloch-Kato's exponential map and Perrin-Riou's "big" exponential map purely in terms of (\phi,\Gamma)-modules over the Robba ring. We first generalize the definition of Bloch-Kato's exponential map for…

Let $p$ be a prime, and let $K$ be a finite extension of $\mathbf{Q}_p$, with absolute Galois group $\cal{G}_K$. Let $\pi$ be a uniformizer of $K$ and let $K_\infty$ be the Kummer extension obtained by adjoining to $K$ a system of…

The purpose of this article is to give formulas for Bloch-Kato's exponential map and its dual for an absolutely crystalline p-adic representation V, in terms of the (phi,Gamma)-module associated to that representation. As a corollary of…

The aim of this article is to generalize Kato's (commutative) p-adic local epsilon-conjecture [Ka93b] for families of (phi,Gamma)-modules over the Robba ring. In particular, we prove the generalized local epsilon-conjecture for rank one…

Let $K$ be a finite extension of $\mathbf{Q}_p$. We use the theory of $(\varphi,\Gamma)$-modules in the Lubin-Tate setting to construct some corestriction-compatible families of classes in the cohomology of $V$, for certain representations…

The classification of the local Galois representations using $(\varphi,\Gamma)$-modules by Fontaine has been generalized by Kisin and Ren over the Lubin-Tate extensions of local fields using the theory of $(\varphi_q,\Gamma_{LT})$-modules.…

Let $p$ be a prime number and $K$ a finite unramified extension of $\mathbb{Q}_p$. Let $\pi$ be an admissible smooth mod $p$ representation of $\mathrm{GL}_2(K)$ occurring in some Hecke eigenspaces of the mod $p$ cohomology and…

Inspired by Nakamura's work (arXiv:1305.0880) on $\epsilon$-isomorphisms for $(\varphi,\Gamma)$-modules over (relative) Robba rings with respect to the cyclotomic theory, we formulate an analogous conjecture for $L$-analytic Lubin-Tate…

In this paper, which is the natural continuation and generalization of Fesenko's non-abelian reciprocity map, we extend the theory of Fesenko to infinite $APF$-Galois extensions $L$ over a local field $K$, with finite residue-class field…

Let $K$ be a finite extension of $\mathbf{Q}_p$ and let $G_K = \mathrm{Gal}(\bar{\mathbf{Q}}_p/K)$. There is a very useful classification of $p$-adic representations of $G_K$ in terms of cyclotomic $(\varphi,\Gamma)$-modules (cyclotomic…

Given a p-adic representation of the Galois group of a local field, we show that its Galois cohomology can be computed using the associated etale (phi,Gamma)-module over the Robba ring; this is a variant of a result of Herr. We then…

Let $p$ be a prime, let $K$ be a finite extension of $\mathbb{Q}_p$, and let $n$ be a positive integer. We construct equivalences of categories between continuous $p$-adic representations of the $n$-fold product of the absolute Galois group…

A classical result of Cherbonnier and Colmez says that all \'etale $(\varphi, \Gamma)$-modules are overconvergent. In this paper, we give another proof of this fact when the base field $K$ is a finite extension of $\mathbb Q_p$.…

Explicit descriptions of local integral Galois module generators in certain extensions of $p$-adic fields due to Pickett have recently been used to make progress with open questions on integral Galois module structure in wildly ramified…

Given a number field $k$, we show that, for many finite groups $G$, all the Galois extensions of $k$ with Galois group $G$ cannot be obtained by specializing any given finitely many Galois extensions $E/k(T)$ with Galois group $G$ and $E/k$…

The construction of the $p$-adic local Langlands correspondence for $\mathrm{GL}_2(\mathbf{Q}_p)$ uses in an essential way Fontaine's theory of cyclotomic $(\varphi,\Gamma)$-modules. Here \emph{cyclotomic} means that $\Gamma =…

We present a generalization of Galois descent to finite modular normal field extension $L/K$, using the Heerma-Galois group $Aut(L[\bar{X}]/K[\bar{X}])$ where $L[\bar{X}]=L[X]/(X^{p^e})$ and $e$ is the exponent of $L$ over $K$.

In this article we extend work of Herr from the case of cyclotomic $(\varphi,\Gamma)$-modules to the general case of Lubin-Tate $(\varphi,\Gamma)$-modules. In particular, we define generalized $\varphi$- and $\psi$-Herr complexes, which…

Let $E/F$ be a cyclic Galois extension of degree $p^l$ with Galois group $G$. It is shown that the Galois module structure of both sides of the Kummer pairing (for Kummer extensions of $E$) are the same. In other words, we show that the…

Let p be an odd prime number and K be a p-adic field. In this paper, we develop an analogue of Fontaine's theory of (phi,Gamma)-modules replacing the p-cyclotomic extension by the extension K_infty obtained by adding to K a compatible…