BIRS Workshop Lecture Videos

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BIRS Workshop Lecture Videos

Rational points and derived equivalence Frei, Sarah


It is natural to ask which properties of a smooth projective variety are recovered by its derived category. In this talk, I will consider the question: is the existence of a rational point preserved under derived equivalence In recent joint work with Nicolas Addington, Benjamin Antieau, and Katrina Honigs, we show that over Q, the answer is no. We give two examples: an abelian variety and a torsor over it, and a pair of hyperkaehler fourfolds. The latter is independently interesting as a new example of a transcendental Brauer-Manin obstruction to the Hasse principle.

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