Journal of the Institute of Mathematics of Jussieu

Table of Contents - October 2012 - Volume 11, Issue 04  

Research Article

On the S-fundamental group scheme. II

Adrian Langera1

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 (alan@mimuw.edu.pl)

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.

(Received June 30 2010)

(Revised December 10 2010)

(Accepted December 23 2010)

Keywords

  • fundamental group;
  • complete variety;
  • positive characteristic;
  • numerically flat bundles

AMS 2010 Mathematics subject classification

  • Primary 14J60;
  • 14F05;
  • 14L15