Semistable sheaves on homogeneous spaces and abelian varieties

Mehta, V. B. ; Nori, M. V. (1984) Semistable sheaves on homogeneous spaces and abelian varieties Proceedings of the Indian Academy of Sciences - Mathematical Sciences, 93 (1). pp. 1-12. ISSN 0253-4142

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In this paper we prove that semistable sheaves with zero Chern classes on homogeneous spaces are trivial and semistable sheaves on abelian varieties with zero Chern classes are filtered by line bundles numerically equivalent to zero. The method consists in reducing mod p and then showing that the Frobenius morphism preserves semistability on the above class of varieties. For technical reasons, we have to assume boundedness of semistable sheaves in char p.

Item Type:Article
Source:Copyright of this article belongs to Indian Academy of Sciences.
Keywords:Semistable Sheaf; Homogeneous Space; Abelian Variety; Frobenius Morphism; Purely Inseparable Descent
ID Code:20417
Deposited On:20 Nov 2010 14:32
Last Modified:17 May 2016 04:45

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