Counting rational points on varieties with large fundamental groupMPIM

by Marco Maculan (Paris)

Thursday Jan 16, 2025, 10:30 AM → 12:00 PM Europe/Berlin

MPIM, Vivatsgasse, 7 - Lecture Hall (Max Planck Institute for Mathematics)

Seminar Algebraic Geometry (SAG)

A nonsingular projective curve of genus at least 2 on a number field admits only finitely many rational points. Elliptic curves might have infinitely many rational points (as the projective line does), but “way less” than the projective line. In a joint work with Y. Brunebarbe, inspired by a recent result of Ellenberg-Lawrence-Venkatesh, we prove an analogous statement in higher dimension: projective varieties with large fundamental group in the sense of Kollár have “way less” rational points than Fano varieties.