Related papers: Relative $(\varphi,\Gamma)$-modules and prismatic …

For a locally finitely presented Grothendieck category $\mathcal{A}$, we consider a certain subcategory of the homotopy category of FP-injective objects in $\mathcal{A}$ which we show is compactly generated. In the case where $\mathcal{A}$…

For a commutative ring $A$, we have the category of (bounded-below) chain complexes of $A$-modules $Ch_{+}(A\mymod)$, a closed symmetric monoidal category with a compatible stable Quillen model structure. The associated homotopy category is…

Let G be the group of L-rational points of a connected split reductive group over a finite extension L of Q_p. We show that formal models of the algebraic flag variety X of G are D-affine for certain sheaves of arithmetic differential…

For a proper, smooth scheme $X$ over a $p$-adic field $K$, we show that any proper, flat, semistable $\mathcal{O}_K$-model $\mathcal{X}$ of $X$ whose logarithmic de Rham cohomology is torsion free determines the same $\mathcal{O}_K$-lattice…

Let $\frak a$, $\frak b$ be ideals of a commutative Noetherian ring $R$ and let $M$, $N$ be finite $R$-modules. The concept of an $\frak a$-filter grade of $\frak b$ on $M$ is introduced and several characterizations and properties of this…

For a commutative ring $S$ and self-orthogonal subcategory $\mathsf{C}$ of $\mathsf{Mod}(S)$, we consider matrix factorizations whose modules belong to $\mathsf{C}$. Let $f\in S$ be a regular element. If $f$ is $M$-regular for every $M\in…

In this paper, we introduce variants of formal nearby cycles for a locally noetherian formal scheme over a complete discrete valuation ring. If the formal scheme is locally algebraizable, then our nearby cycle gives a generalization of…

For a proper semistable curve $X$ over a DVR of mixed characteristics we reprove the "invariant cycles theorem" with trivial coefficients (see Chiarellotto, 1999) i.e. that the group of elements annihilated by the monodromy operator on the…

We prove embeddings of adelic groups on an excellent scheme of special type and a flat quasicoherent sheaf on it. For a normal excellent scheme of special type we establish the equality…

Let k be a perfect field of characteristic p>0. When p>2, Fontaine and Laffaille have classified p-divisibles groups and finite flat p-groups over the Witt vectors W(k) in terms of filtered modules. Still assuming p>2, we extend these…

We define the i-restriction and i-induction functors on the category O of the cyclotomic rational double affine Hecke algebras. This yields a crystal on the set of isomorphism classes of simple modules, which is isomorphic to the crystal of…

We derive a relative version of the local monodromy theorem for ordinary differential equations on an annulus over a mixed-characteristic nonarchimedean field, and give several applications in $p$-adic cohomology and $p$-adic Hodge theory.…

Let $\mathfrak a$ denote an ideal of a local ring $(R, \mathfrak m).$ Let $M$ be a finitely generated $R$-module. There is a systematic study of the formal cohomology modules $\varprojlim \HH^i(M/\mathfrak a^nM), i \in \mathbb Z.$ We…

We construct the $\Lambda$-adic de Rham analogue of Hida's ordinary $\Lambda$-adic \'etale cohomology and of Ohta's $\Lambda$-adic Hodge cohomology, and by exploiting the geometry of integral models of modular curves over the cyclotomic…

Let k be a commutative ring with unit. We endow the categories of filtered complexes and of bicomplexes of k-modules, with cofibrantly generated model structures, where the class of weak equivalences is given by those morphisms inducing a…

Given a Henselian and Japanese discrete valuation ring $A$ and a flat and projective $A$-scheme $X$, we follow the approach of Biswas-dos Santos to introduce a full subcategory of coherent modules on $X$ which is then shown to be Tannakian.…

Let $\mathcal{T}$ be an $\mathcal{O}_K$-linear idempotent-complete, small smooth proper stable $\infty$-category, where $K$ is a finite extension of $\mathbb{Q}_p$. We give a Breuil-Kisin module structure on the topological negative cyclic…

Given a perfect field $k$ of characteristic $p>0$, a smooth proper $k$-scheme $Y$, a crystal $E$ on $Y$ relative to $W(k)$ and a finite group $G$ acting on $Y$ and $E$, we show that, viewed as virtual $k[G]$-module, the reduction modulo $p$…

We generalize a result of Orlov and Van den Bergh on the representability of a cohomological functor from the bounded derived category of a smooth projective variety over a field to the category of L-modules, to the case where L is a field…

We prove that the category of systems of sesquilinear forms over a given hermitian category is equivalent to the category of unimodular 1-hermitian forms over another hermitian category. The sesquilinear forms are not required to be…