Related papers: A note on \'etale $(\varphi,\Gamma)$-modules in fa…

We introduce the notion of completed $F$-crystals on the absolute prismatic site of a smooth $p$-adic formal scheme. We define a functor from the category of completed prismatic $F$-crystals to that of crystalline \'etale…

We propose a p-adic Langlands correspondence in families.

Let $X$ be an integral model at a prime $p$ of a Shimura variety of PEL type having good reduction, associated to a reductive group $G$. To $\mathbb{Z}_p$ reprsententations of the group $G$ can be associated two kinds of sheaves : crystals…

We review the analog of Fontaine's theory of crystalline $p$-adic Galois representations and their classification by weakly admissible filtered isocrystals in the arithmetic of function fields over a finite field. There crystalline Galois…

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…

In this paper, we apply stack theoretic ideas to the classification problem in Dieudonn\'e theory. First, we use crystalline cohomology of classifying stacks to directly reconstruct the classical Dieudonn\'e module of a finite, $p$-power…

Let $K$ be a complete discretely valued field with mixed characteristic $(0, p)$ and imperfect residue field $k_K$. Let $\Delta$ be a finite set. We construct an equivalence of categories between finite dimensional…

We construct cohomology theories for $(\varphi, \tau)$-modules, and study their relation with cohomology of $(\varphi, \Gamma)$-modules, as well as Galois cohomology. Our method is axiomatic, and can treat the \'etale case, the…

Let $X$ be a smooth scheme over a finite field of characteristic $p$. In answer to a conjecture of Deligne, we establish that for any prime $\ell \neq p$, an $\ell$-adic Weil sheaf on $X$ which is algebraic (or irreducible with finite…

In local relative $p$-adic Hodge theory, we show that the Galois cohomology of a finite height crystalline representation (up to a twist) is essentially computed via the (Fontaine--Messing) syntomic complex with coefficients in the…

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 $Y/S$ be a $p$-completely smooth morphism of $p$-torsion free $p$-adic formal schemes endowed with a Frobenius lift, and let $\overline Y/\overline S$ denote its reduction modulo $p$. We show that the category of crystals on the…

We prove that if $G$ is a finite flat group scheme of $p$ power rank over a perfect field of characteristic $p$, then the second crystalline cohomology of its classifying stack $H^2_{crys}(BG)$ recovers the Dieudonn\'e module of $G$. We…

In this paper, we define and construct canonical filtered $F$-crystals with $G$-structure over the integral models for Shimura varieties of abelian type at hyperspecial level defined by Kisin. We check that these are related by $p$-adic…

Let $p$ be a prime and $K$ be a $p$-adic local field. We study the stack of quasi-deRham $(\varphi,\Gamma_K)$-modules, i.e. $(\varphi,\Gamma_K)$-modules that are deRham up to twist by characters. These objects are used to construct and then…

We prove a number of results on the \'etale cohomology of rigid analytic varieties over $p$-adic non-archimedean local fields. Among other things, we establish bounds for Frobenius eigenvalues, show a strong version of Grothendieck's local…

We show an equivalence of categories, over general $p$-adic bases, between finite locally $p^n$-torsion commutative group schemes and $\Int/p^n\Int$-modules in perfect $F$-gauges of Tor amplitude $[-1,0]$ with Hodge-Tate weights $0,1$. By…

In this paper we explain how to attach to a family of $p$-adic representations of a product of Galois groups an overconvergent family of multivariable $(\varphi,\Gamma)$-modules, generalizing results from Pal-Zabradi and…

By the theory of Colmez and Fontaine, a de Rham representation of the Galois group of a local field roughly corresponds to a representation of the Weil-Deligne group equipped with an admissible filtration on the underlying vector space.…

Let $p$ be a prime number, $K$ a finite unramified extension of $\mathbb{Q}_p$ and $\mathbb{F}$ a finite extension of $\mathbb{F}_p$. Using perfectoid spaces we associate to any finite-dimensional continuous representation $\overline{\rho}$…