English
 
Help Privacy Policy Disclaimer
  Advanced SearchBrowse

Item

ITEM ACTIONSEXPORT

Released

Journal Article

Decompositions of derived categories of gerbes and of families of Brauer-Severi varieties

MPS-Authors
/persons/resource/persons234952

Bergh,  Daniel
Max Planck Institute for Mathematics, Max Planck Society;

External Resource
Fulltext (restricted access)
There are currently no full texts shared for your IP range.
Supplementary Material (public)
There is no public supplementary material available
Citation

Bergh, D., & Schnürer, O. M. (2021). Decompositions of derived categories of gerbes and of families of Brauer-Severi varieties. Documenta Mathematica, 26, 1465-1500. doi:10.25537/dm.2021v26.1465-1500.


Cite as: https://hdl.handle.net/21.11116/0000-000A-D2EE-D
Abstract
It is well known that the category of quasi-coherent sheaves on a gerbe banded by a diagonalizable group decomposes according to the characters of the group. We establish the corresponding decomposition of the unbounded derived category of complexes of sheaves with quasi-coherent cohomology. This generalizes earlier work by Lieblich for gerbes over schemes whereas our gerbes may live over arbitrary algebraic stacks. \par By combining this decomposition with the semi-orthogonal decomposition for a projectivized vector bundle, we deduce a semi-orthogonal decomposition of the derived category of a family of Brauer-Severi varieties whose components can be described in terms of twisted sheaves on the base. This reproves and generalizes a result of Bernardara.