Vanishing theorems for constructible sheaves on abelian varieties
We show that the hypercohomology of most character twists of perverse sheaves on a complex abelian variety vanishes in all non-zero degrees. As a consequence we obtain a vanishing theorem for constructible sheaves and a relative vanishing theorem for a homomorphism between abelian varieties. Our pro...
Gespeichert in:
| Hauptverfasser: | , |
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| Dokumenttyp: | Article (Journal) |
| Sprache: | Englisch |
| Veröffentlicht: |
April 20, 2015
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| In: |
Journal of algebraic geometry
Year: 2015, Jahrgang: 24, Heft: 3, Pages: 531-568 |
| ISSN: | 1534-7486 |
| DOI: | 10.1090/jag/645 |
| Online-Zugang: | Verlag, Volltext: http://dx.doi.org/10.1090/jag/645
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| Verfasserangaben: | Thomas Krämer and Rainer Weissauer |
MARC
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| 520 | |a We show that the hypercohomology of most character twists of perverse sheaves on a complex abelian variety vanishes in all non-zero degrees. As a consequence we obtain a vanishing theorem for constructible sheaves and a relative vanishing theorem for a homomorphism between abelian varieties. Our proof relies on a Tannakian description for convolution products of perverse sheaves, and with future applications in mind we discuss the basic properties of the arising Tannaka groups. | ||
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