Graduate Algebraic Geometry Seminar
Fumiaki Suzuki
UIC
O-acyclic varieties without rational points
Abstract: Based on computations over finite fields, Serre asked in a letter to Grothendieck whether a projective variety over the function field of a curve always has a rational point if it is O-acyclic, that is, H^i(X,O)=0 for all i>0. Then Grabber-Harris-Mazur-Starr gave the negative answer to this question by constructing an Enriques surface without rational points. Later, more explicit constructions of such Enriques surfaces were given by Lafon and Starr. We are going to discuss these examples and related problems.
Wednesday September 18, 2019 at 5:00 PM in 712 SEO