Related papers: Prismatic Dieudonn\'e theory

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 construct a relative version of the $A_{\rm inf}$-cohomology theory developed by Bhatt-Morrow-Scholze and relate it to the prismatic theory of Bhatt-Scholze. The construction relies on the fiber product of topoi. As an application we…

We establish a comparison isomorphism between prismatic cohomology and derived de Rham cohomology respecting various structures, such as their Frobenius actions and filtrations. As an application, when $X$ is a proper smooth formal scheme…

We show an equivalence between the two categories in the title, thus establishing a link between Frobenius-linear objects of formal (schematic) and analytic (adic) nature. We will do this for arbitrary p-complete rings, arbitrary…

In this paper, we develop the notion of presentability in the parametrised homotopy theory framework of Barwick-Dotto-Glasman-Nardin-Shah over orbital categories. We formulate and prove a characterisation of parametrised presentable…

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…

We put the theory of interacting topological crystalline phases on a systematic footing. These are topological phases protected by space-group symmetries. Our central tool is an elucidation of what it means to "gauge" such symmetries. We…

Let $k$ be an algebraically closed field of characteristic $p>0$, let $R$ be a commutative ring, and let $\mathbb{F}$ be an algebraically closed field of characteristic 0. We consider the $R$-linear category $\mathcal{F}^\Delta_{Rpp_k}$ of…

The question of when the derived category of a ring satisfies Brown--Adams representability is revisited via studying the transfer of pure homological dimension along definable functors: it is shown that, for any ring, the pure global…

Long ago, Fontaine formulated conjectures (now theorems) relating \'etale and de Rham cohomologies of algebraic varieties over $p$-adic fields. In an earlier work we have shown that pro-\'etale and de Rham cohomologies of analytic varieties…

For a $p$-divisible group $G$ over a smooth projective variety $X$ over $k$, where $k$ is a field finitely generated over a perfect field of characteristic $p$, we show that the formal group $R^i f_{\fppf*} G$ is isogenous to a…

We develop a theory of derived rigid spaces and quasi-coherent sheaves and analytic "stratifications" on them. Amongst other things, we obtain a six-functor formalism for these quasi-coherent sheaves and analytic stratifications. We provide…

For an algebraically closed non-archimedean extension $C/\mathbb{Q}_p$, we define a Tannakian category of $p$-adic Hodge structures over $C$ that is a local, $p$-adic analog of the global, archimedean category of $\mathbb{Q}$-Hodge…

We define the motivic filtrations on real topological Hochschild homology and its companions. In particular, we prove that real topological cyclic homology admits a natural complete filtration whose graded pieces are equivariant suspensions…

We introduce the notion of a $p$-Cartier smooth algebra. It generalises that of a smooth algebra and includes valuation rings over a perfectoid base. We give several characterisations of $p$-Cartier smoothness in terms of prismatic…

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…

In this paper, we prove that for any $p$-adic smooth separated formal scheme $\mathfrak X$, the category of prismatic $F$-crystals with $I$ inverted is equivalent to the category of \'etale $\mathbb Z_p$-local systems on the generic fiber…

Let X be a smooth p-adic formal scheme. We show that integral crystalline local systems on the generic fiber of X are equivalent to prismatic F-crystals over the analytic locus of the prismatic site of X. As an application, we give a…

We introduce a bicategory that refines the localization of the category of dg categories with respect to quasi-equivalences and investigate its properties via formal category theory. Concretely, we first introduce the bicategory of dg…

Let $\frakX$ be a smooth $p$-adic formal scheme over $\calO_K$ with adic generic fiber $X$. We obtain a global equivalence between the category $\Vect((\frakX)_{\Prism},\overline\calO_{\Prism}[\frac{1}{p}])$ of rational Hodge--Tate crystals…