Related papers: Relative p-adic Hodge theory: Foundations

For a curve C and a reductive group G in prime characteristic, we relate the de Rham moduli of logarithmic G-connections on C to the Dolbeault moduli of logarithmic G-Higgs bundles on the Frobenius twist of C. We name this result the…

We recall some basic constructions from p-adic Hodge theory, then describe some recent results in the subject. We chiefly discuss the notion of B-pairs, introduced recently by Berger, which provides a natural enlargement of the category of…

For any smooth proper rigid analytic space $X$ over a complete algebraically closed extension of $\mathbb Q_p$, we construct a $p$-adic Simpson correspondence: an equivalence of categories between vector bundles on Scholze's pro-\'etale…

The goal of this paper is to construct the p-adic analytic family of overconvergent half-integral weight modular forms using Hecke-equivariant overconvergent Shintani lifting. The classical Shintani map is the Hecke-equivariant map from the…

The notion of a p-adic de Rham representation of the absolute Galois group of a p-adic field was introduced about twenty years ago (see e.g. [Fo93]). Three important results for this theory have been obtained recently: The structure theorem…

We start with a curve over an algebraically closed ground field of positive characteristic $p>0$. By using specialization techniques, under suitable natural coprimality conditions, we prove a cohomological Simpson Correspondence between the…

For a field of characteristic $\ne 2$ we study vector spaces that are graded by the weight lattice of a root system, and are endowed with linear operators in each simple root direction. We show that these data extend to a graded semisimple…

We use Scholze's framework of diamonds to gain new insights in correspondences between $p$-adic vector bundles and local systems. Such correspondences arise in the context of $p$-adic Simpson theory in the case of vanishing Higgs fields. In…

Let $k$ be a perfect field of characteristic $p > 2$. We extend the equivalence of categories between Fontaine-Laffaille modules and $\mathbb{Z}_p$ lattices inside crystalline representations with Hodge-Tate weights at most $p-2$ of…

We prove that any projective coadmissible module over the locally analytic distribution algebra of a compact $p$-adic Lie group is finitely generated. In particular, the category of coadmissible modules does not have enough projectives. In…

In this paper we investigate the arithmetic aspects of the theory of $\mathcal{E}_K^\dagger$-valued rigid cohomology introduced and studied in [11,12]. In particular we show that these cohomology groups have compatible connections and…

We show that geometric syntomic cohomology lifts canonically to the category of Banach-Colmez spaces and study its relation to extensions of modifications of vector bundles on the Fargues-Fontaine curve. We include some computations of…

We use the $p$-divisible group attached to a 1-motive to generalize the conjugate $p$-adic uniformization of Iovita--Morrow--Zaharescu to arbitrary $p$-adic formal semi-abelian schemes or $p$-divisible groups over the ring of integers in a…

The classical Witt vectors are a ubiquitous object in algebra and number theory. They arise as a functorial construction that takes perfect fields k of prime characteristic p > 0 to p-adically complete discrete valuation rings of…

Sen attached to each p-adic Galois representation of a p-adic field a multiset of numbers called generalized Hodge-Tate weights. In this paper, we discuss a rigidity of these numbers in a geometric family. More precisely, we consider a…

The main result of this paper is the existence of Galois representations associated with the mod $p$ (or mod $p^m$) cohomology of the locally symmetric spaces for $\GL_n$ over a totally real or CM field, proving conjectures of Ash and…

We interpret syntomic cohomology of Nekov\'a\v{r}-Nizio{\l} as a $p$-adic absolute Hodge cohomology. This is analogous to the interpretation of Deligne-Beilinson cohomology as an absolute Hodge cohomology by Beilinson and generalizes the…

This paper studies the derived de Rham cohomology of F_p and p-adic schemes, and is inspired by Beilinson's recent work. Generalising work of Illusie, we construct a natural isomorphism between derived de Rham cohomology and crystalline…

We construct a $p$-adic $L$-function for $P$-ordinary Hida families of cuspidal automorphic representations on a unitary group $G$. The main new idea of our work is to incorporate the theory of Schneider-Zink types for the Levi quotient of…

Andr\'e used Hodge-theoretic methods to show that in a smooth proper family X to B of varieties over an algebraically closed field k of characteristic 0, there exists a closed fiber having the same Picard number as the geometric generic…