Mathematics – Algebraic Geometry
Scientific paper
2009-12-14
Mathematics
Algebraic Geometry
v2: simplified proof of the main theorem and added section computing S-fundamental group scheme of a variety with trivial etal
Scientific paper
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.
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