Related papers: The derived $\infty$-category of Cartier Modules

We construct a canonical pseudofunctor ^# on the category of finite-type maps of (say) connected noetherian universally catenary finite-dimensional separated schemes, taking values in the category of Cousin complexes. This pseudofunctor is…

Let $\mathcal{C}$ be a finite tensor category and $\mathcal{M}$ an exact left $\mathcal{C}$-module category. We call $\mathcal{M}$ unimodular if the finite multitensor category ${\sf Rex}_{\mathcal{C}}(\mathcal{M})$ of right exact…

We prove that an enriched $\infty$-category is completely determined by its enriched presheaf category together with a `marking' by the representable presheaves. More precisely, for any presentably monoidal $\infty$-category $\mathcal{V}$…

In this article we introduce a slight modification of the definition of test modules which is an additive functor $\tau$ on the category of coherent Cartier modules. We show that in many situations this modification agrees with the usual…

To each category C of modules of finite length over a complex simple Lie algebra g, closed under tensoring with finite dimensional modules, we associate and study a category Aff(C)_\kappa of smooth modules (in the sense of Kazhdan and…

Functors involved in Fontaine equivalences decompose as extension of scalars and taking of invariants between full subcategories of modules over a topological ring equipped with semi-linear continuous action of a topological monoid. We give…

Given a cartesian closed category $\mathcal{V}$, we introduce an internal category of elements $\int_\mathcal{C} F$ associated to a $\mathcal{V}$-functor $F\colon \mathcal{C}^{\mathrm{op}}\to \mathcal{V}$. When $\mathcal{V}$ is extensive,…

We investigate the stabilization $\mathcal{S}$ of the module category over an artinian ring $\Lambda$ by formally inverting the tensor endofunctor given by the bimodule of relative noncommutative differential $1$-forms. It turns out that…

We introduce a framework for pulling back Cartier modules and their associated invariants along regular $F$-finite morphisms. To achieve this, we construct a relative Cartier isomorphism and operator for an arbitrary regular $F$-finite map…

Given a symmetric monoidal stable $\infty$-category $\mathcal{C}$ and a left adjoint symmetric monoidal fiber functor to $\operatorname{Mod}_A^{\otimes}$ for some $\mathbb{E}_{\infty}$-ring $A$, one can construct a derived group scheme $G$…

We contribute to the classification of modular categories $\mathcal{C}$ with $\operatorname{FPdim}(\mathcal{C})\equiv 2 \pmod 4$. We prove that such categories have group of invertibles of even order, and that they factorize as $\mathcal…

In this paper we introduce a notion of $\mathbf{O}$-monoidal $\infty$-categories for a finite sequence $\mathbf{O}^{\otimes}$ of $\infty$-operads, which is a generalization of the notion of higher monoidal categories in the setting of…

Let $R$ be a commutative Noetherian ring and let $\mathcal D(R)$ be its (unbounded) derived category. We show that all compactly generated t-structures in $\mathcal D(R)$ associated to a left bounded filtration by supports of Spec$(R)$ have…

We prove that the $\infty$-category of $p$-typical topological Cartier modules, recently introduced by Antieau--Nikolaus, over some base $A$ is equivalent to the $\infty$-category of modules over a ring spectrum $\mathcal R_A$, which we…

For a nice-enough category $\mathcal{C}$, we construct both the morphism category ${\rm H}(\mathcal{C})$ of $\mathcal{C}$ and the category ${\rm mod}\mbox{-}\mathcal{C}$ of all finitely presented contravariant additive functors over…

The Grothendieck construction is a classical correspondence between diagrams of categories and coCartesian fibrations over the indexing category. In this paper we consider the analogous correspondence in the setting of model categories. As…

The aim of this paper is to unify classification theories of torsion classes of finite dimensional algebras and commutative Noetherian rings. For a commutative Noetherian ring $R$ and a module-finite $R$-algebra $\Lambda$, we study the set…

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 $\mathcal{A}$…

Let $\mathcal{V}$ be a mixed characteristic complete discrete valuation ring, $\mathcal{P}$ a separated smooth formal scheme over $\mathcal{V}$, $P$ its special fiber, $X$ a smooth closed subscheme of $P$, $T$ a divisor in $P$ such that…

Making use of Freyd's free abelian category on a preadditive category we show that if $T:D\rightarrow \mathcal{A}$ is a representation of a quiver $D$ in an abelian category $\mathcal{A}$ then there is an abelian category $\mathcal{A} (T)$,…