English

On the fundamental group scheme of rationally chain connected varieties

Algebraic Geometry 2015-05-22 v2

Abstract

Let kk be an algebraically closed field. Chambert-Loir proved that the \'etale fundamental group of a normal rationally chain connected variety over kk is finite. We prove that the fundamental group scheme of a normal rationally chain connected variety over kk is finite and \'etale. In particular, the fundamental group scheme of a Fano variety is finite and \'etale.

Keywords

Cite

@article{arxiv.1410.1166,
  title  = {On the fundamental group scheme of rationally chain connected varieties},
  author = {Marco Antei and Indranil Biswas},
  journal= {arXiv preprint arXiv:1410.1166},
  year   = {2015}
}

Comments

Final version in International Mathematics Research Notices, 2015