Related papers: Serre functors and local duality for affine quotie…

We construct a quasi-coherent sheaf of associative algebras which controls a category of $AV$-modules over a smooth quasi-projective variety. We establish a local structure theorem, proving that in \'etale charts these associative algebras…

When a reductive group $G$ acts linearly on a complex projective scheme $X$ there is a stratification of $X$ into $G$-invariant locally closed subschemes, with an open stratum $X^{ss}$ formed by the semistable points in the sense of…

We prove that the entropy of the Serre functor $\mathbb{S}$ in the partially wrapped Fukaya category of a graded surface $\Sigma$ with stops is given by the function sending $t \in \mathbb{R}$ to $ h_t(\mathbb{S}) = (1-\min \Omega)t$, for…

We introduce a formalism to produce several families of spectral sequences involving the derived functors of the limit and colimit functors over a finite partially ordered set. The first type of spectral sequences involves the left derived…

We provide a categorical interpretation of a well-known identity from linear algebra as an isomorphism of certain functors between triangulated categories arising from finite dimensional algebras. As a consequence, we deduce that the Serre…

The goal of this papers is to extending to the complex analytic framework the relative Kleiman duality for quasi coherent sheaves. Precisely, he show that for any flat,locally projectivea and finitely presented morphism of schemes…

We give a necessary and sufficient condition for non-local functionals on vector-valued Lebesgue spaces to be weakly sequentially lower semi-continuous. Here a non-local functional shall have the form of a double integral of a density which…

We study regularity in the context of ring spectra and spectral stacks. Parallel to that, we construct a weight structure on the category of compact quasi-coherent sheaves on spectral quotient stacks of the form $X=[\operatorname{Spec}…

We introduce a new method to compute explicit formulae for various zeta functions associated to groups and rings. The specific form of these formulae enables us to deduce local functional equations. More precisely, we prove local functional…

In this paper, we study Serre's condition $(S_n)$ for tensor products of modules over a commutative noetherian local ring. The paper aims to show the following. Let $M$ and $N$ be finitely generated module over a commutative noetherian…

In this paper, we classify several subcategories of the category of coherent sheaves on a noetherian divisorial scheme (e.g. a quasi-projective scheme over a commutative noetherian ring). More precisely, we classify the torsionfree (resp.…

We present a functorial computation of the equivariant intersection cohomology of a hypertoric variety, and endow it with a natural ring structure. When the hyperplane arrangement associated with the hypertoric variety is unimodular, we…

We give criteria for the existence of a Serre functor on the derived category of a gauged Landau-Ginzburg model. This is used to provide a general theorem on the existence of an admissible (fractional) Calabi-Yau subcategory of a gauged…

We study the spectrum of closed subcategories in a quasi-scheme, i.e. a Grothendieck category $X$. The closed subcategories are the direct analogs of closed subschemes in the commutative case, in the sense that when $X$ is the category of…

We study the 0-th local cohomology module of the jacobian ring of a singular reduced complex projective hypersurface X, by relating it to the sheaf of logarithmic vector field along X. We investigate the analogies between the local…

This is a report on recent work of Chalupnik and Touze. We explain the Koszul duality for the category of strict polynomial functors and make explicit the underlying monoidal structure which seems to be of independent interest. Then we…

For a field $E$ of characteristic different from $2$ and cohomological $2$-dimension one, quadratic forms over the rational function field $E(X)$ are studied. A characterisation in terms of polynomials in $E[X]$ is obtained for having that…

We prove a Cartier duality for gerbes of algebraic and analytic vector bundles as an anti-equivalence of Hopf algebras in the category of kernels of analytic stacks. As an application, we prove that the category of solid quasi-coherent…

Given an algebraic stack $X$, one may compare the derived category of quasi-coherent sheaves on $X$ with the category of dg-modules over the dg-ring of functions on $X$. We study the analogous question in stable homotopy theory, for derived…

If $X$ is a quasi-compact and quasi-separated scheme, the category $Qcoh(X)$ of quasi-coherent sheaves on $X$ is locally finitely presented. Therefore categorical flat quasi-coherent sheaves naturally arise. But there is also the standard…