Anti-affine groups

Abstract

Recall that a scheme X is said to be anti-affine if $\mathcal{O}\left( X \right) = k$. In this chapter, we obtain characterizations of anti-affine group schemes, and we describe their structure and classification. The results that we present were obtained in [Bri09] and in [SS09], via two different approaches that are both valid over any base field. Here we mostly follow the former approach, with some simplifications.