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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 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

Des propriétés de finitude des foncteurs polynomiaux

Aurélien Djament (2016)

Fundamenta Mathematicae

We study finiteness properties, especially the noetherian property, the Krull dimension and a variation of finite presentation, in categories of polynomial functors (notion introduced by Djament and Vespa) from a small symmetric monoidal category whose unit is an initial object to an abelian category. We prove in particular that the category of polynomial functors from the category of free abelian groups ℤⁿ with split monomorphisms to abelian groups is "almost" locally noetherian. We also give an...

Descent equivalence

Xiuzhan Guo, Manuela Sobral, Walter Tholen (2004)

Cahiers de Topologie et Géométrie Différentielle Catégoriques

Descent for monads.

Hofstra, Pieter, De Marchi, Federico (2006)

Theory and Applications of Categories [electronic only]

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