Related papers: Derived equivalence and non-vanishing loci

Lurie's representability theorem gives necessary and sufficient conditions for a functor to be an almost finitely presented derived geometric stack. We establish several variants of Lurie's theorem, making the hypotheses easier to verify…

We prove that if two abelian varieties have equivalent derived categories then the derived categories of the smooth stacks associated to the corresponding Kummer varieties are equivalent as well. The second main result establishes necessary…

We study the derived invariance of the cohomology theories $Hoch^*$, $H^*$ and $HC^*$ associated to coalgebras over a field. We prove a theorem characterizing derived equivalences. As particular cases, it describes the two following…

We discuss the homological algebra of representation theory of finite dimensional algebras and finite groups. We present various methods for the construction and the study of equivalences of derived categories: local group theory, geometry…

We prove that smooth projective varieties with equivalent derived categories have isogenous (and sometimes isomorphic) Picard varieties. In particular their irregularity and number of independent vector fields are the same. This is turn…

In this work, we explore links between natural homology and persistent homology for the classification of directed spaces. The former is an algebraic invariant of directed spaces, a semantic model of concurrent programs. The latter was…

We explicitly describe cohomology of the sheaf of differential forms with poles along a semiample divisor on a complete simplicial toric variety. As an application, we obtain a new vanishing theorem which is an analogue of the…

Unlike in the case of distinguishable particles, the concept of entanglement-- not to mention, nonlocality-- remains debated in case of indistinguishable particles. Here, we show that certain existing all-versus-nothing type of proofs of…

Contrary to the expected behavior, we show the existence of non-invertible deformations of Lie algebras which can generate invariants for the coadjoint representation, as well as delete cohomology with values in the trivial or adjoint…

In the paper we answer the following question: for a morphism of varieties (or, more generally, stacks), when the derived category of the base can be recovered from the derived category of the covering variety by means of descent theory? As…

In this paper we construct new derived invariants with integral coefficients using the theory of motifs, and give several applications. Specifically, we obtain the following results: For complex algebraic surfaces, we prove that certain…

We prove an equivalence between the derived category of a variety and the equivariant/graded singularity category of a corresponding singular variety. The equivalence also holds at the dg level.

In this paper, we prove the integrality conjecture for quotient stacks arising from weakly symmetric representations of reductive groups. Our main result is a decomposition of the cohomology of the stack into finite-dimensional components…

We reprove and generalize the result that the intersection cohomology groups of a toric variety with coefficient in a nontrivial rank one local system vanish. We prove a similar vanishing result for a certain class of varieties on which a…

We construct a notion of derived completion which applies to homomorphisms of commutative S-algebras. We study the relationship of the construction with other constructions of completions, and prove various invariance properties. The…

We show that a proof in multiplicative linear logic can be represented as a decorated surface, such that two proofs are logically equivalent just when their surfaces are geometrically equivalent. This is an extended abstract for…

We introduce a theoretical framework for differentiable surface evolution that allows discrete topology changes through the use of topological derivatives for variational optimization of image functionals. While prior methods for inverse…

In this paper, we will consider derived equivalences for differential graded endomorphism algebras by Keller's approaches. First we construct derived equivalences of differential graded algebras which are endomorphism algebras of the…

We give a characterisation of functors whose induced functor on the level of localisations is an equivalence and where the isomorphism inverse is induced by some kind of replacements such as projective resolutions or cofibrant replacements.

We consider derived categories of coherent sheaves on smooth projective varieties. We prove that any equivalence between them can be represented by an object on the product. Using this, we give a necessary and sufficient condition for…