Decompositions of derived categories of gerbes and of families of Brauer-Severi varieties
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- Decompositions of Derived Categories of Gerbes
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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.
Original language | English |
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Journal | Documenta Mathematica |
Volume | 26 |
Pages (from-to) | 1465-1500 |
ISSN | 1431-0635 |
DOIs | |
Publication status | Published - 2021 |
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ID: 300777587