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numerically flat bundles

Journal of the Institute of Mathematics of Jussieu (1)

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On the S-fundamental group scheme. II
Part of
Adrian Langer
Journal:

Journal of the Institute of Mathematics of Jussieu / Volume 11 / Issue 4 / October 2012

Published online by Cambridge University Press:

02 April 2012, pp. 835-854

Print publication:

October 2012
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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.