SAG: On the Euler characteristic of ordinary irregular varietiesPublic Event

by Jefferson Baudin (EPFL)

Thursday Dec 11, 2025, 10:30 AM → 12:30 PM Europe/Berlin

MPIM, Vivatsgasse, 7 - Conference Room (Max Planck Institute for Mathematics)

Over the complex numbers, a useful tool to study the geometry of irregular varieties is generic vanishing. This has led to several remarkable results: characterization of abelian varieties by only fixing a few invariants, deeper understanding of the Euler characteristic of irregular varieties, study of their pluricanonical systems, and so on.

These theorems rely on vanishing results of analytic nature, making this whole topic harder to reach in positive characteristic. Our goal in this talk will be to explain how generic vanishing works in positive characteristic, through the prism of the study of Euler characteristics. We will present the following theorem: if X is a smooth projective ordinary variety of maximal Albanese dimension (i.e. dim(alb(X)) = dim(X)), then the Euler characteristic of the sheaf of top forms is non-negative. If in addition this quantity is zero, then the Albanese image of X is fibered by abelian varieties.

The proof uses the positive characteristic generic vanishing theory developed by Hacon-Patakfalvi, as well as our recent Witt vector version of Grauert-Riemenschneider vanishing.