Seminar Algebra & Geometry: Costa Shramov
Automorphisms of pointless surfaces
I will speak about finite groups acting by birational automorphisms of surfaces over algebraically non-closed fields, mostly function fields. One of important observations here is that a smooth geometrically rational surface S is either birational to a product of a projective line and a conic (in particular, S is rational provided that it has a point), or finite subgroups of its birational automorphism group are bounded.
We will also discuss some particular types of surfaces with interesting automorphism groups, including Severi-Brauer surfaces.