相关论文: Prismatic crystals over the de Rham period sheaf

We study Hodge-Tate crystals on the absolute (log-) prismatic site of $\mathcal{O}_K$, where $\mathcal{O}_K$ is a mixed characteristic complete discrete valuation ring with perfect residue field. We first classify Hodge-Tate crystals by…

We systematically study relative and absolute ${\Delta}_{\mathrm{dR}}^+$-crystals on the (log-) prismatic site of a smooth (resp.~ semi-stable) formal scheme. Using explicit computation of stratifications, we classify (local) relative…

Let $\mathcal{O}_K$ be a mixed characteristic complete DVR with perfect residue field $k$ and fraction field $K$. It is a celebrated result of Berthelot and Ogus that for a smooth proper formal scheme $X/\mathcal{O}_K$ there exists a…

Let $X=\mathrm{Spf}(\mathcal{O}_K)$. We classify perfect complexes of $n$-truncated prismatic crystals on the prismatic site of $X$ when $n\leq 1+\frac{p-1}{e}$ by studying perfect complexes on the $n$-truncated prismatization of $X$, which…

Let $\mathcal{O}_{K}$ be a complete discrete valuation ring of mixed characteristic with perfect residue field, endowed with its canonical log-structure. We prove that log $p$-divisible groups over $\mathcal{O}_{K}$ correspond to…

We study de Rham prismatic crystals on $(\mathcal{O}_K)_{\bbold{\Delta}}$. We show that a de Rham crystal is controlled by a sequence of matrices $\{A_{m,1}\}_{m \geq 0}$ with $A_{0,1}$ "nilpotent". Using this, we prove that the natural…

Let $K$ be a mixed characteristic complete discrete valuation field with perfect residue field, and let $K_\infty/K$ be a Kummer tower extension by adjoining a compatible system of $p$-power roots of a chosen uniformizer. We use this Kummer…

Let $K|\mathbb{Q}_p$ be a complete discrete valuation field with perfect residue field, $O_K$ be its ring of integers. Consider a semistable $p$-adic formal scheme $X$ over $\mathrm{Spf}(O_K)$ with smooth generic fiber $X_{\eta}$.…

Let $(A, I)$ be a bounded prism, and $X$ be a smooth $p$-adic formal scheme over $\Spf(A/I)$. We consider the notion of crystals on Bhatt--Scholze's prismatic site $(X/A)_{\prism}$ of $X$ relative to $A$. We prove that if $X$ is proper over…

In this paper, we consider the (crystalline) prismatic crystals on a scheme $\mathfrak{X}$. We classify the crystals by $p$-connections on a certain ring and prove a cohomological comparison theorem. This equivalence is more general than…

We study the algebraic $K$-theory of rings of the form $R[x]/x^e$. We do this via trace methods and filtrations on topological Hochschild homology and related theories by quasisyntomic sheaves. We produce computations for $R$ a perfectoid…

Let $\mathbf{B}_{\mathrm{dR}}^{+, \dagger} \subset \mathbf{B}_{\mathrm{dR}}^{+}$ be the ``convergent" de Rham period ring which is the (un-completed) stalk at the de Rham point of the Fargues--Fontaine curve. We develop a Tate--Sen…

We define, for each quasi-syntomic ring $R$ (in the sense of Bhatt-Morrow-Scholze), a category $\mathrm{DM}^{\rm adm}(R)$ of \textit{admissible prismatic Dieudonn\'e crystals over $R$} and a natural functor from $p$-divisible groups over…

We investigate $p$-adic cohomologies of log rigid analytic varieties over a $p$-adic field. For a log rigid analytic variety $X$ defined over a discretely valued field, we compute the Kummer pro-\'etale cohomology of…

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…

Let $Y$ be a locally complete intersection over $\mathcal{O}_K$ containing a $p$-power root of unity $\zeta_p$. We classify the derived category of prismatic crystals on the absolute prismatic site of $Y$ by studying quasi-coherent…

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…

In this article we give an interpretation, in terms of derived de Rham complexes, of Scholze's de Rham period sheaf and Tan--Tong's crystalline period sheaf.

Let $K$ be a complete discretely valued field of mixed characteristic $(0,p)$ with perfect residue field. We prove that the category of prismatic $F$-crystals on $\mathcal O_K$ is equivalent to the category of lattices in crystalline…

Let $K$ be a complete discretely valued field of mixed characteristic $(0,p)$ with perfect residue field, and let $E$ be a finite extension of $\mathbf{Q}_p$ contained in $K$. We show that the category of prismatic $F$-crystals on…