a1 Institute of Mathematics, Warsaw University, ul. Banacha 2, 02–097 Warsaw, Poland and Institute of Mathematics, Polish Academy of Sciences, ul. Śniadeckich 8, 00–956 Warsaw, Poland (email@example.com)
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 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 étale fundamental group.
(Received June 30 2010)
(Revised December 10 2010)
(Accepted December 23 2010)
AMS 2010 Mathematics subject classification