English

Anti-affine algebraic groups

Algebraic Geometry 2008-06-25 v3 Group Theory

Abstract

We say that an algebraic group GG over a field is anti-affine if every regular function on GG is constant. We obtain a classification of these groups, with applications to the structure of algebraic groups in positive characteristics, and to the construction of many counterexamples to Hilbert's fourteenth problem.

Keywords

Cite

@article{arxiv.0710.5211,
  title  = {Anti-affine algebraic groups},
  author = {Michel Brion},
  journal= {arXiv preprint arXiv:0710.5211},
  year   = {2008}
}

Comments

Prior work of Carlos Sancho de Salas acknowledged, additional minor changes,

R2 v1 2026-06-21T09:37:06.553Z