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Mat. Sb., 2012, Volume 203, Number 5, Pages 33–64 (Mi msb7790)  

This article is cited in 4 scientific papers (total in 4 papers)

Descent theory for semiorthogonal decompositions

A. Elaginab

a A. A. Kharkevich Institute for Information Transmission Problems, Russian Academy of Sciences
b National Research University "Higher School of Economics"

Abstract: We put forward a method for constructing semiorthogonal decompositions of the derived category of $G$-equivariant sheaves on a variety $X$ under the assumption that the derived category of sheaves on $X$ admits a semiorthogonal decomposition with components preserved by the action of the group $G$ on $X$. This method is used to obtain semiorthogonal decompositions of equivariant derived categories for projective bundles and blow-ups with a smooth centre as well as for varieties with a full exceptional collection preserved by the group action. Our main technical tool is descent theory for derived categories.
Bibliography: 12 titles.

Keywords: derived category, semiorthogonal decomposition, descent theory, algebraic variety.

DOI: https://doi.org/10.4213/sm7790

Full text: PDF file (674 kB)
References: PDF file   HTML file

English version:
Sbornik: Mathematics, 2012, 203:5, 645–676

Bibliographic databases:

UDC: 512.73
MSC: Primary 14F05, 18C15; Secondary 13D09, 18E30
Received: 15.09.2010 and 12.08.2011

Citation: A. Elagin, “Descent theory for semiorthogonal decompositions”, Mat. Sb., 203:5 (2012), 33–64; Sb. Math., 203:5 (2012), 645–676

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. A. Kuznetsov, A. Perry, “Derived categories of cyclic covers and their branch divisors”, Selecta Math. (N.S.), 23:1 (2017), 389–423  mathnet  crossref  mathscinet  zmath  isi  scopus
    2. Tabuada G., “Equivariant Noncommutative Motives”, Ann. K-Theory, 3:1 (2018), 125–156  crossref  mathscinet  zmath  isi
    3. Auel A. Bernardara M., “Semiorthogonal Decompositions and Birational Geometry of Del Pezzo Surfaces Over Arbitrary Fields”, Proc. London Math. Soc., 117:1 (2018), 1–64  crossref  mathscinet  zmath  isi  scopus
    4. Shinder E., “Group Actions on Categories and Elagin'S Theorem Revisited”, Eur. J. Math., 4:1, 1, SI (2018), 413–422  crossref  mathscinet  zmath  isi  scopus
  • Математический сборник Sbornik: Mathematics (from 1967)
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