# Sofia Tirabassi: Rational points and (twisted) derived equivalence

**Time: **
Wed 2019-02-13 13.15 - 14.15

**Location: **
Room 3418, KTH

**Participating: **
Sofia Tirabassi (SU)

Abstract: Is the existence of rational point a (twisted) derived invariant? This question was asked by Hasset and Tschinkel who give affirmative answer in some untwisted cases. On the other hand Asher, Dasaratha, Perry and Zhou provide an examples of twisted equivalent K3 surfaces over Q such that only one of them has a rational point. My aim for this talk is twofold. On one side, I will present an untwisted example which answers negatively to Hasset-Tschinkel. On the other side I will try to convince you as, for varieties over finite fields, the existence of a rational point should be a twisted derived invariant. This is a joint work (wildly in progress) with Addington, Antieau and Honigs.