Speaker: Mathieu Florence (University of Paris, Jussieu)
Title: Abelian varieties as automorphism groups
Abstract: Let X be a smooth projective variety over a field F. Automorphisms of X are then represented by a group scheme over F, denoted by Aut(X). Conversely, given an algebraic group G over F, it is natural to ask whether G=Aut(X), for some smooth projective F-variety X. This question is the topic of active current investigation. Using analytical techniques, Lombardo and Maffei recently showed the following. Assume that G=A is an abelian variety, and that F=C is the field of complex numbers. Then, A=Aut(X) for some smooth projective X/F, if and only if A/F has finitely many group automorphisms. Their result was extended to all algebraically closed fields F by Blanc and Brion. In this talk, I will extend it further, to the case of an arbitrary field F. Note that the same question, when G/F is a linear algebraic group, is wide open.
Zoom details: https://osu.zoom.us/j/97909959308?pwd=QWNZeTY0UUlVQWNlODV1Q2J4TWpGUT09
Meeting Id: 979 0995 9308, Passcode: 752011
