𝐹-divided sheaves trivialized by dominant maps are essentially finite

Tonini, Fabio; Zhang, Lei

doi:10.1090/tran/7444

$F$-divided sheaves trivialized by dominant maps are essentially finite
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by Fabio Tonini and Lei Zhang PDF

Trans. Amer. Math. Soc. 371 (2019), 5529-5549 Request permission

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 nonproper nonsmooth algebraic stacks over arbitrary fields of characteristic $p>0$. As a byproduct 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.

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