Fumiaki Suzuki : O-acyclic varieties without rational points

Posted by Gregory Taylor , part of the Graduate Algebraic Geometry Seminar.

At

Sept. 18, 2019, 5 p.m.

In

712 SEO

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.