Biswas, Indranil ; Parameswaran, A. J. ; Subramanian, S.
(2011)
*Essentially finite vector bundles on varieties with trivial tangent bundle*
Proceedings of the American Mathematical Society, 139
.
pp. 3821-3829.
ISSN 0002-9939

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Official URL: http://www.ams.org/journals/proc/2011-139-11/S0002...

Related URL: http://dx.doi.org/10.1090/S0002-9939-2011-10804-9

## Abstract

Let X be a smooth projective variety, defined over an algebraically closed field of positive characteristic, such that the tangent bundle TX is trivial. Let F_{X}: X→X be the absolute Frobenius morphism of X. We prove that for any n≥1 , the n-fold composition F_{X}_{n} is a torsor over X for a finite group-scheme that depends on n. For any vector bundle E→X, we show that the direct image F_{X}_{n}∗E is essentially finite (respectively, F-trivial) if and only if E is essentially finite (respectively, F-trivial).

Item Type: | Article |
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Source: | Copyright of this article belongs to American Mathematical Society. |

ID Code: | 87689 |

Deposited On: | 20 Mar 2012 14:10 |

Last Modified: | 27 Jun 2012 13:47 |

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