Decomposition of the Grothendieck group of stable categories of finite groups.
Deformations and derived categories
In this paper we generalize the deformation theory of representations of a profinite group developed by Schlessinger and Mazur to deformations of objects of the derived category of bounded complexes of pseudocompact modules for such a group. We show that such objects have versal deformations under certain natural conditions, and we find a sufficient condition for these versal deformations to be universal. Moreover, we consider applications to deforming Galois cohomology classes and the étale hypercohomology...
Deligne-Lusztig restriction of a Gelfand-Graev module
Using Deodhar’s decomposition of a double Schubert cell, we study the regular representations of finite groups of Lie type arising in the cohomology of Deligne-Lusztig varieties associated to tori. We deduce that the Deligne-Lusztig restriction of a Gelfand-Graev module is a shifted Gelfand-Graev module.
Derived categories and the analytic approach to general reciprocity laws. I.
Derived categories and the analytic approach to general reciprocity laws. III.
Derived categories and the analytic approach to general reciprocity laws. II.
Derived categories of coherent sheaves on rational homogeneous manifolds.
Derived category of toric varieties with small Picard number
This paper aims to construct a full strongly exceptional collection of line bundles in the derived category D b(X), where X is the blow up of ℙn−r ×ℙr along a multilinear subspace ℙn−r−1×ℙr−1 of codimension 2 of ℙn−r ×ℙr. As a main tool we use the splitting of the Frobenius direct image of line bundles on toric varieties.
Derived endo-discrete artin algebras
Let Λ be an artin algebra. We prove that for each sequence of non-negative integers there are only a finite number of isomorphism classes of indecomposables , the bounded derived category of Λ, with for all i ∈ ℤ and E(X) the endomorphism ring of X in if and only if , the bounded derived category of the category of all left Λ-modules, has no generic objects in the sense of [4].
Derived equivalence classification of weakly symmetric algebras of domestic type
We complete the derived equivalence classification of all weakly symmetric algebras of domestic type over an algebraically closed field, by solving the problem of distinguishing standard and nonstandard algebras up to stable equivalence, and hence derived equivalence. As a consequence, a complete stable equivalence classification of weakly symmetric algebras of domestic type is obtained.
Derived equivalence for cyclic blocks over a P-adic ring.
Derived quot schemes
Derived tubular algebras and APR-tilts
Deriving DG categories
Determinantal Barlow surfaces and phantom categories
We prove that the bounded derived category of the surface constructed by Barlow admits a length 11 exceptional sequence consisting of (explicit) line bundles. Moreover, we show that in a small neighbourhood of in the moduli space of determinantal Barlow surfaces, the generic surface has a semiorthogonal decomposition of its derived category into a length 11 exceptional sequence of line bundles and a category with trivial Grothendieck group and Hochschild homology, called a phantom category....
Distinguishing derived equivalence classes using the second Hochschild cohomology group
We study the second Hochschild cohomology group of the preprojective algebra of type D₄ over an algebraically closed field K of characteristic 2. We also calculate the second Hochschild cohomology group of a non-standard algebra which arises as a socle deformation of this preprojective algebra and so show that the two algebras are not derived equivalent. This answers a question raised by Holm and Skowroński.
Dualité relative en géométrie analytique complexe.