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.

arXiv commentminor corrections; 46 pages

References in corpus (8)

• Jordan property for groups of birational selfmaps
• Jordan property for non-linear algebraic groups and projective varieties
• Topologies and structures of the Cremona groups
• Jordan property for automorphism groups of compact spaces in Fujiki's class $C$
• Jordan property for algebraic groups and automorphism groups of projective varieties in arbitrary characteristic
• Birational splitting and algebraic group actions
• Numerically trivial automorphisms of Enriques surfaces in characteristic $2$
• Automorphism group schemes of bielliptic and quasi-bielliptic surfaces

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