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

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Decompositions of derived categories of gerbes and of families of Brauer-Severi varieties. / Bergh, Daniel Sven Tobias; Schnürer, Olaf M.

In: Documenta Mathematica, Vol. 26, 2021, p. 1465-1500 .

Research output: Contribution to journal › Journal article › Research › peer-review

Harvard

Bergh, DST & Schnürer, OM 2021, 'Decompositions of derived categories of gerbes and of families of Brauer-Severi varieties', Documenta Mathematica, vol. 26, pp. 1465-1500 . https://doi.org/10.25537/dm.2021v26.1465-1500

APA

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

Vancouver

Bergh DST, Schnürer OM. Decompositions of derived categories of gerbes and of families of Brauer-Severi varieties. Documenta Mathematica. 2021;26:1465-1500 . https://doi.org/10.25537/dm.2021v26.1465-1500

Author

Bergh, Daniel Sven Tobias ; Schnürer, Olaf M. / Decompositions of derived categories of gerbes and of families of Brauer-Severi varieties. In: Documenta Mathematica. 2021 ; Vol. 26. pp. 1465-1500 .

Bibtex

@article{5e08c115f20440999e434992e4bbaf7e,
title = "Decompositions of derived categories of gerbes and of families of Brauer-Severi varieties",
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.",
author = "Bergh, {Daniel Sven Tobias} and Schn{\"u}rer, {Olaf M.}",
year = "2021",
doi = "10.25537/dm.2021v26.1465-1500",
language = "English",
volume = "26",
pages = "1465--1500 ",
journal = "Documenta Mathematica",
issn = "1431-0635",
publisher = "Deutsche Mathematiker Vereinigung",

}

RIS

TY - JOUR

T1 - Decompositions of derived categories of gerbes and of families of Brauer-Severi varieties

AU - Bergh, Daniel Sven Tobias

AU - Schnürer, Olaf M.

PY - 2021

Y1 - 2021

N2 - 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.

AB - 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.

U2 - 10.25537/dm.2021v26.1465-1500

DO - 10.25537/dm.2021v26.1465-1500

M3 - Journal article

VL - 26

SP - 1465

EP - 1500

JO - Documenta Mathematica

JF - Documenta Mathematica

SN - 1431-0635

ER -

ID: 300777587