Related papers: Morita theory for stable derivators

We formalize, at the level of D-modules, the notion that A-hypergeometric systems are equivariant versions of the classical hypergeometric equations. For this purpose, we construct a functor on a suitable category of torus equivariant…

The aim of this work is to construct certain homotopy t-structures on various categories of motivic homotopy theory, extending works of Voevodsky, Morel, D\'eglise and Ayoub. We prove these $t$-structures possess many good properties, some…

In this paper we consider an effective divisor on the complex projective line and associate with it the module D consisting of all the derivations $\theta$ such that $\theta(I_i)\subset I_i^{m_i}$ for every $i$, where $I_i$ is the ideal of…

We extend Orlov's result that certain functors between derived categories of smooth projective varieties are Fourier--Mukai transforms to the case when those varieties are smooth and proper.

We consider the effect of $t$-structures on the Tannaka duality theory for dg categories developed in our previous paper. We associate non-negative dg coalgebras $C$ to dg functors on the hearts of $t$-structures, and relate dg…

In this paper, we show that stable functors of derived equivalences preserve the isomorphism classes of versal deformation rings of finitely generated Gorenstein-projective modules over finite dimensional $k$-algebras. Then we generalize…

We prove that arbitrary pullbacks, as well as Betti and \'etale realisation functors, are t-exact for the constructible motivic t-structure on the category of cohomological 1-motives over a base scheme.

Stable equivalences of Morita type preserve many interesting properties and is proved to be the appropriate concept to study for equivalences between stable categories. Recently the singularity category attained much attraction and Xiao-Wu…

Let $\mathcal{A}$ be an abelian category and $\mathcal{B}$ be the Happel-Reiten-Smal{\o} tilt of $\mathcal{A}$ with respect to a torsion pair. We give necessary and sufficient conditions for the existence of a derived equivalence between…

Tambara functors are equivariant analogues of rings arising in representation theory and equivariant homotopy theory. We introduce the notion of a clarified Tambara functor and show that under mild conditions every Tambara functor admits a…

Variables are a crucial element in logic and are also addressed in institution theory, an effort to axiomatize logic. In institution theory, we typically use extensions (signature morphisms) obtained from variables instead of introducing…

We link smooth Artin motives to \'etale local systems and Artin representations. We then construct the ordinary motivic t-structure on Artin motives with integral coefficients and show that the $\ell$-adic realization functor is t-exact.

By results of Rognerud, a source algebra equivalence between two $p$-blocks of finite groups induces an equivalence between the categories of cohomological Mackey functors associated with these blocks, and a splendid derived equivalence…

We study when the heart of a t-structure in a triangulated category $\mathcal{D}$ with coproducts is AB5 or a Grothendieck category. If $\mathcal{D}$ satisfies Brown representability, a t-structure has an AB5 heart with an injective…

We prove that if two associative deformations (parameterized by the same complete local ring) are derived Morita equivalent, then they are Morita equivalent (in the classical sense).

We introduce the notion of noncompact (partial) silting and (partial) tilting sets and objects in any triangulated category D with arbitrary (set-indexed) coproducts. We show that equivalence classes of partial silting sets are in bijection…

The structure of the category of matroids and strong maps is investigated: it has coproducts and equalizers, but not products or coequalizers; there are functors from the categories of graphs and vector spaces, the latter being faithful;…

By results of the second author, a source algebra equivalence between two $p$-blocks of finite groups induces an equivalence between the categories of cohomological Mackey functors associated with these blocks, and a splendid derived…

Let $k$ be a field of characteristic zero, $\CO$ be a dg operad over $k$ and let $A$ be an $\CO$-algebra. In this note we define formal deformations of $A$, construct the deformation functor $$\Def_A:\dgar(k)\to\simpl$$ from the category of…

We prove a Decomposition Theorem for the direct image of an irreducible local system on a smooth complex projective variety under a morphism with values in another smooth complex projective variety. For this purpose, we construct a category…