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On the S-fundamental group scheme. II

Part of: Algebraic groups Surfaces and higher-dimensional varieties (Co)homology theory

Published online by Cambridge University Press:  02 April 2012

Adrian Langer
Adrian Langer
Affiliation:
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 (alan@mimuw.edu.pl)
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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 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.

Keywords

fundamental groupcomplete varietypositive characteristicnumerically flat bundles

MSC classification

Secondary: 14J60: Vector bundles on surfaces and higher-dimensional varieties, and their moduli 14F05: Sheaves, derived categories of sheaves and related constructions 14L15: Group schemes
Type
Research Article
Information
Journal of the Institute of Mathematics of Jussieu , Volume 11 , Issue 4 , October 2012 , pp. 835 - 854
Copyright
Copyright © Cambridge University Press 2012

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