Geodesic
Decompositions of derived categories of gerbes and of families of Brauer-Severi varieties
Documenta mathematica, Tome 26 (2021), pp. 1465-1500 Cet article a éte moissonné depuis la source EMS Press

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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.
DOI : 10.4171/dm/846
Classification : 14A20, 14F08
Mots-clés : derived category, gerbe, semi-orthogonal decomposition, algebraic stack, Brauer-Severi variety 
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     author = {Daniel Bergh and Olaf M. Schn\"urer},
     title = {Decompositions of derived categories of gerbes and of families of {Brauer-Severi} varieties},
     journal = {Documenta mathematica},
     pages = {1465--1500},
     year = {2021},
     volume = {26},
     doi = {10.4171/dm/846},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/dm/846/}
}
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Daniel Bergh; Olaf M. Schnürer. Decompositions of derived categories of gerbes and of families of Brauer-Severi varieties. Documenta mathematica, Tome 26 (2021), pp. 1465-1500. doi: 10.4171/dm/846

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