Intermediate Jacobians and rationality over arbitrary fields

Abstract: Clemens and Griffiths have used intermediate Jacobians to show that smooth cubic threefolds are irrational. In this talk, I will explain how to extend the Clemens-Griffiths method over arbitrary fields. As an application, I will show that a three-dimensional smooth complete intersection of two quadrics over a field $\mathbb k$ is $\mathbb k$-rational if and only if it contains a line defined over $\mathbb k$. This is joint work with Olivier Wittenberg.

Russianalgebraic geometry

Audience: researchers in the topic

Iskovskikh seminar

Series comments: Description: Seminar