On the S-fundamental group scheme II

Abstract

The S-fundamental group scheme is the group scheme corresponding to the Tannaka category of numerically flat vector bundles. We use determinant line bundles to prove that the S-fundamental group of a product of two complete varieties is a product of their S-fundamental groups as conjectured by V. Mehta and the author. We also compute the abelian part of the S-fundamental group scheme and the S-fundamental group scheme of an abelian variety or a variety with trivial etale fundamental group.

v2: simplified proof of the main theorem and added section computing S-fundamental group scheme of a variety with trivial etale fundamental group via Esnault-Mehta method; v3: 20 pages, numerous corrections and clarifications; to appear in J. Inst. Math. Jussieu

References in corpus (1)

• Simply connected projective manifolds in characteristic $p>0$ have no nontrivial stratified bundles

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