Decompositions of derived categories of gerbes and of families of Brauer-Severi varieties
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 ge...
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| creator | Bergh, Daniel Schnürer, Olaf M |
| description | 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.
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 familiy 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. |
| doi_str_mv | 10.48550/arxiv.1901.08945 |
| format | Article |
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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.
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 familiy 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.</description><identifier>DOI: 10.48550/arxiv.1901.08945</identifier><language>eng</language><subject>Mathematics - Algebraic Geometry</subject><creationdate>2019-01</creationdate><rights>http://arxiv.org/licenses/nonexclusive-distrib/1.0</rights><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>228,230,780,885</link.rule.ids><linktorsrc>$$Uhttps://arxiv.org/abs/1901.08945$$EView_record_in_Cornell_University$$FView_record_in_$$GCornell_University$$Hfree_for_read</linktorsrc><backlink>$$Uhttps://doi.org/10.48550/arXiv.1901.08945$$DView paper in arXiv$$Hfree_for_read</backlink></links><search><creatorcontrib>Bergh, Daniel</creatorcontrib><creatorcontrib>Schnürer, Olaf M</creatorcontrib><title>Decompositions of derived categories of gerbes and of families of Brauer-Severi varieties</title><description>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.
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 familiy 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.</description><subject>Mathematics - Algebraic Geometry</subject><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2019</creationdate><recordtype>article</recordtype><sourceid>GOX</sourceid><recordid>eNotj81uwjAQhH3poaI8QE_kBZLaMV4nR0rpj4TEAS6coo29RpYIRk4atW9fk3KanR3NSB9jz4IXy0op_oLxx4-FqLkoeFUv1SM7vpEJ3TX0fvDh0mfBZZaiH8lmBgc6hehp-p4otunCi705h50_35PXiN8U8z2NqZiNmBpDip7Yg8NzT_O7ztjhfXNYf-bb3cfXerXNEbTKa4scBLbgwEnUkisEpaFsdWl4UqUrWQtBUJVOoTbWCrTccCNBtQgkZ2zxPzuxNdfoO4y_zY2xmRjlH41UTPs</recordid><startdate>20190125</startdate><enddate>20190125</enddate><creator>Bergh, Daniel</creator><creator>Schnürer, Olaf M</creator><scope>AKZ</scope><scope>GOX</scope></search><sort><creationdate>20190125</creationdate><title>Decompositions of derived categories of gerbes and of families of Brauer-Severi varieties</title><author>Bergh, Daniel ; Schnürer, Olaf M</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-a675-9da061ab6f6f3a7305a65762b72c07625783911e682f5a7cdd1ad0c0c365ba6e3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2019</creationdate><topic>Mathematics - Algebraic Geometry</topic><toplevel>online_resources</toplevel><creatorcontrib>Bergh, Daniel</creatorcontrib><creatorcontrib>Schnürer, Olaf M</creatorcontrib><collection>arXiv Mathematics</collection><collection>arXiv.org</collection></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext_linktorsrc</fulltext></delivery><addata><au>Bergh, Daniel</au><au>Schnürer, Olaf M</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Decompositions of derived categories of gerbes and of families of Brauer-Severi varieties</atitle><date>2019-01-25</date><risdate>2019</risdate><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.
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 familiy 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.</abstract><doi>10.48550/arxiv.1901.08945</doi><oa>free_for_read</oa></addata></record> |
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| subjects | Mathematics - Algebraic Geometry |
| title | Decompositions of derived categories of gerbes and of families of Brauer-Severi varieties |
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