Cohomological descent theory for a morphism of stacks and for equivariant derived categories

Journal Article · Sat Apr 30 04:00:00 EDT 2011 · Sbornik. Mathematics

DOI:https://doi.org/10.1070/SM2011V202N04ABEH004153; COUNTRY OF INPUT: INTERNATIONAL ATOMIC ENERGY AGENCY (IAEA)· OSTI ID:21592552

Elagin, Alexei D ^[1]

---

1. A. A. Kharkevich Institute for Information Transmission Problems, Russian Academy of Sciences, Moscow (Russian Federation)

In the paper, we find necessary and sufficient conditions under which, if X{yields}S is a morphism of algebraic varieties (or, in a more general case, of stacks), the derived category of S can be recovered by using the tools of descent theory from the derived category of X. We show that for an action of a linearly reductive algebraic group G on a scheme X this result implies the equivalence of the derived category of G-equivariant sheaves on X and the category of objects in the derived category of sheaves on X with a given action of G on each object. Bibliography: 18 titles.

• OSTI ID: 21592552
• Journal Information: Sbornik. Mathematics, Journal Name: Sbornik. Mathematics Journal Issue: 4 Vol. 202; ISSN 1064-5616
• Country of Publication: United States
• Language: English

Related Subjects

97 MATHEMATICS AND COMPUTING
ALGEBRA
EVOLUTION
GROUP THEORY
MATHEMATICAL EVOLUTION
MATHEMATICAL LOGIC
MATHEMATICAL MANIFOLDS
MATHEMATICS