Automorphisms of surfaces over fields of positive characteristic

Abstract

We study automorphism and birational automorphism groups of varieties over fields of positive characteristic from the point of view of Jordan and $p$-Jordan property. In particular, we show that the Cremona group of rank $2$ over a field of characteristic $p>0$ is $p$-Jordan, and the birational automorphism group of an arbitrary geometrically irreducible algebraic surface is nilpotently $p$-Jordan of class at most $2$. Also, we show that the automorphism group of a smooth geometrically irreducible projective variety of non-negative Kodaira dimension is Jordan in the usual sense.

minor corrections; 46 pages

References in corpus (1)

• Jordan property for automorphism groups of compact spaces in Fujiki's class $C$

Cited by in corpus (3)

• Birational automorphism groups of Severi-Brauer surfaces over the field of rational numbers
• Automorphism groups of $P^1$-bundles over a non-uniruled base
• The most symmetric smooth cubic surface