相关论文: A stacky comparison of the Hodge and Nygaard filtr…

We use the stacky approach to $p$-adic cohomology theories recently developed by Drinfeld and Bhatt--Lurie to generalise known comparison theorems in $p$-adic Hodge theory so as to accommodate coefficients. More precisely, we establish a…

We use the stacky approach to $p$-adic cohomology theories recently developed by Drinfeld and Bhatt--Lurie to generalise a comparison theorem between the rational crystalline cohomology of the special fibre and the rational $p$-adic \'etale…

This work is devoted to the study of integral $p$-adic Hodge theory in the context of Artin stacks. For a Hodge-proper stack, using the formalism of prismatic cohomology, we establish a version of $p$-adic Hodge theory with the \'etale…

We continue to study the logarithmic prismatic cohomology defined by the first author, and complete the proof of the de Rham comparison and \'etale comparison generalizing those of Bhatt and Scholze. We prove these comparisons for a derived…

We give a new proof of a recent result of Tong Liu, which gives a general control on the torsion in the graded pieces of the so-called integral Hodge filtration associated to a crystalline Galois lattice. Our approach is stack-theoretic,…

Let $k$ be a field of characteristic $p,$ and $f : X \to S$ a smooth proper morphism of smooth $k$-schemes. Katz's formula gives a relationship between the Kodaira--Spencer map of $f,$ and an invariant called the $p$-curvature of the…

We look more closely at the higher nonabelian de Rham cohomology of a smooth projective variety or family of varieties that had been defined in some previous papers. We formalize using $n$-stacks the notion of shape underlying this…

This article gives an expository account of quasisyntomic descent and the Nygaard filtration in positive characteristic, complemented by several new applications to $p$-adic cohomology theories. The guiding result is a new approach to…

We study a cohomology theory for rigid-analytic varieties over $\mathbb{C}_p$, without properness or smoothness assumptions, taking values in filtered quasi-coherent complexes over the Fargues-Fontaine curve, which compares to other…

We define and initiate the study of analytic de Rham stacks of relative Fargues-Fontaine curves. To this end, we develop a theory of analytic de Rham stacks with sufficiently strong descent and approximation properties. Specializing to the…

We use the Beilinson $t$-structure on filtered complexes and the Hochschild-Kostant-Rosenberg theorem to construct filtrations on the negative cyclic and periodic cyclic homologies of a scheme $X$ with graded pieces given by the…

Faltings' approach in $p$-adic Hodge theory can be schematically divided into two main steps: firstly, a local reduction of the computation of the $p$-adic \'etale cohomology of a smooth variety over a $p$-adic local field to a Galois…

The purpose of this paper is to prove a basic $p$-adic comparison theorem for smooth rigid analytic and dagger varieties over the algebraic closure $C$ of a $p$-adic field: $p$-adic pro-\'etale cohomology, in a stable range, can be…

We extend the construction of A$_{\rm inf}$-cohomology by Bhatt-Morrow-Scholze to the context of log $p$-adic formal schemes over a log perfectoid base. In particular, using coordinates, we prove comparison theorems between log A$_{\rm…

In this paper, we complete the nonabelian Hodge theory (NAHT) triangle of isomorphisms for stacks between the Borel-Moore homologies of the Dolbeault, Betti, and de Rham moduli stacks. We first explain how to realise the category of…

We construct Hodge filtered cohomology groups for complex manifolds that combine the topological information of generalized cohomology theories with geometric data of Hodge filtered holomorphic forms. This theory provides a natural…

Inspired by Bhatt-Morrow-Scholze's work on ${\rm THH}$, we define Nygaard-completed log prismatic cohomology based on log topological Hochschild homology via filtrations on log ${\rm THH}$ and its variants. Moreover, of independent…

We construct a new cohomology theory for proper smooth (formal) schemes over the ring of integers of C_p. It takes values in a mixed-characteristic analogue of Dieudonne modules, which was previously defined by Fargues as a version of…

We compute, in a stable range, the arithmetic p-adic etale cohomology of smooth rigid analytic and dagger varieties (without any assumption on the existence of a nice integral model) in terms of differential forms using syntomic methods.…

The aim of this article is to given an extension of the prismatization functor for $p$-adic formal schemes (whose construction was first sketched by Drinfeld and then given by Bhatt-Lurie) to all schemes over $\mathrm{Spec}(\mathbf{Z})$. We…