By a result of Biswas and Dos Santos, on a smooth and projective variety over an algebraically closed field, a vector bundle trivialized by a proper and surjective map is essentially finite, that is it corresponds to a representation of the Nori fundamental group scheme. In this paper we obtain similar results for non-proper non-smooth algebraic stacks over arbitrary fields of characteristic p ą 0. As by-product we have the following partial generalization of the Biswas-Dos Santos’ result in positive characteristic: on a pseudo-proper and inflexible stack of finite type over k a vector bundle which is trivialized by a proper and flat map is essentially finite.

$F$-divided sheaves trivialized by dominant maps are essentially finite / Tonini, Fabio; Zhang, Lei. - In: TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY. - ISSN 0002-9947. - ELETTRONICO. - 371:(2019), pp. 5529-5549. [10.1090/tran/7444]

$F$-divided sheaves trivialized by dominant maps are essentially finite

Tonini, Fabio;
2019

Abstract

By a result of Biswas and Dos Santos, on a smooth and projective variety over an algebraically closed field, a vector bundle trivialized by a proper and surjective map is essentially finite, that is it corresponds to a representation of the Nori fundamental group scheme. In this paper we obtain similar results for non-proper non-smooth algebraic stacks over arbitrary fields of characteristic p ą 0. As by-product we have the following partial generalization of the Biswas-Dos Santos’ result in positive characteristic: on a pseudo-proper and inflexible stack of finite type over k a vector bundle which is trivialized by a proper and flat map is essentially finite.
371
5529
5549
Tonini, Fabio; Zhang, Lei
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/2158/1156899
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