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

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 $p>0$. 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.

21 pages

References in corpus (2)

• Algebraic and Nori fundamental gerbes
• Fundamental gerbes

Cited by in corpus (3)

• On the fundamental group schemes of certain quotient varieties
• Fundamental gerbes
• An embedding problem for finite local torsors over twisted curves