English

On the S-fundamental group scheme II

Algebraic Geometry 2015-03-24 v3

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 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.

Keywords

Cite

@article{arxiv.0912.2623,
  title  = {On the S-fundamental group scheme II},
  author = {Adrian Langer},
  journal= {arXiv preprint arXiv:0912.2623},
  year   = {2015}
}

Comments

v2: simplified proof of the main theorem and added section computing S-fundamental group scheme of a variety with trivial etale fundamental group via Esnault-Mehta method; v3: 20 pages, numerous corrections and clarifications; to appear in J. Inst. Math. Jussieu

R2 v1 2026-06-21T14:23:30.100Z