|
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:
     
Document Type:
Article
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
\Bibitem{Ela12}
\by A.~Elagin
\paper Descent theory for semiorthogonal decompositions
\jour Mat. Sb.
\yr 2012
\vol 203
\issue 5
\pages 33--64
\mathnet{http://mi.mathnet.ru/msb7790}
\crossref{https://doi.org/10.4213/sm7790}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2976858}
\zmath{https://zbmath.org/?q=an:06084149}
\adsnasa{http://adsabs.harvard.edu/cgi-bin/bib_query?2012SbMat.203..645E}
\elib{http://elibrary.ru/item.asp?id=19066491}
\transl
\jour Sb. Math.
\yr 2012
\vol 203
\issue 5
\pages 645--676
\crossref{https://doi.org/10.1070/SM2012v203n05ABEH004238}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000306361100002}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84863896165}
Linking options:
http://mi.mathnet.ru/eng/msb7790https://doi.org/10.4213/sm7790 http://mi.mathnet.ru/eng/msb/v203/i5/p33
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:
-
A. Kuznetsov, A. Perry, “Derived categories of cyclic covers and their branch divisors”, Selecta Math. (N.S.), 23:1 (2017), 389–423
 -
Tabuada G., “Equivariant Noncommutative Motives”, Ann. K-Theory, 3:1 (2018), 125–156
-
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
-
Shinder E., “Group Actions on Categories and Elagin'S Theorem Revisited”, Eur. J. Math., 4:1, 1, SI (2018), 413–422
|
| Number of views: |
| This page: | 287 | | Full text: | 41 | | References: | 25 | | First page: | 36 |
|
Terms of Use