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

This article is cited in 6 scientific papers (total in 6 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
    5. Sun Ch., “A Note on Equivariantization of Additive Categories and Triangulated Categories”, J. Algebra, 534 (2019), 483–530  crossref  mathscinet  zmath  isi
    6. Bergh D., Schnuerer O.M., “Conservative Descent For Semi-Orthogonal Decompositions”, Adv. Math., 360 (2020), 106882  crossref  mathscinet  zmath  isi
  • Математический сборник Sbornik: Mathematics (from 1967)
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