All a b c d e f g h i j k l m n o p q r s t u v w x y z Other

Previous Page 2 Next

Displaying 21 – 40 of 140

Showing per page

Cluster characters for 2-Calabi–Yau triangulated categories

Yann Palu (2008)

Annales de l’institut Fourier

Starting from an arbitrary cluster-tilting object T in a 2-Calabi–Yau triangulated category over an algebraically closed field, as in the setting of Keller and Reiten, we define, for each object L , a fraction X ( T , L ) using a formula proposed by Caldero and Keller. We show that the map taking L to X ( T , L ) is a cluster character, i.e. that it satisfies a certain multiplication formula. We deduce that it induces a bijection, in the finite and the acyclic case, between the indecomposable rigid objects of the cluster...

Coherent functors in stable homotopy theory

Henning Krause (2002)

Fundamenta Mathematicae

Coherent functors 𝓢 → Ab from a compactly generated triangulated category into the category of abelian groups are studied. This is inspired by Auslander's classical analysis of coherent functors from a fixed abelian category into abelian groups. We characterize coherent functors and their filtered colimits in various ways. In addition, we investigate certain subcategories of 𝓢 which arise from families of coherent functors.

Compact corigid objects in triangulated categories and co-t-structures

David Pauksztello (2008)

Open Mathematics

In the work of Hoshino, Kato and Miyachi, [11], the authors look at t-structures induced by a compact object, C , of a triangulated category, 𝒯 , which is rigid in the sense of Iyama and Yoshino, [12]. Hoshino, Kato and Miyachi show that such an object yields a non-degenerate t-structure on 𝒯 whose heart is equivalent to Mod(End( C )op). Rigid objects in a triangulated category can the thought of as behaving like chain differential graded algebras (DGAs). Analogously, looking at objects which behave...

Deformations and derived categories

Frauke M. Bleher, Ted Chinburg (2005)

Annales de l'institut Fourier

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

Olivier Dudas (2009)

Annales scientifiques de l'École Normale Supérieure

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 category of toric varieties with small Picard number

Laura Costa, Rosa Miró-Roig (2012)

Open Mathematics

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

Raymundo Bautista (2006)

Colloquium Mathematicae

Let Λ be an artin algebra. We prove that for each sequence ( h i ) i ∈ ℤ of non-negative integers there are only a finite number of isomorphism classes of indecomposables X ∈ b ( Λ ) , the bounded derived category of Λ, with l e n g t h E ( X ) H i ( X ) = h i for all i ∈ ℤ and E(X) the endomorphism ring of X in b ( Λ ) if and only if b ( M o d Λ ) , the bounded derived category of the category M o d Λ of all left Λ-modules, has no generic objects in the sense of [4].

Derived equivalence classification of weakly symmetric algebras of domestic type

Rafał Bocian, Andrzej Skowroński (2016)

Colloquium Mathematicae

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 quot schemes

Ionuţ Ciocan-Fontanine, Mikhail Kapranov (2001)

Annales scientifiques de l'École Normale Supérieure

Determinantal Barlow surfaces and phantom categories

Christian Böhning, Hans-Christian Graf von Bothmer, Ludmil Katzarkov, Pawel Sosna (2015)

Journal of the European Mathematical Society

We prove that the bounded derived category of the surface S constructed by Barlow admits a length 11 exceptional sequence consisting of (explicit) line bundles. Moreover, we show that in a small neighbourhood of S 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....

Currently displaying 21 – 40 of 140