Published on *Max Planck Institute for Mathematics* (https://www.mpim-bonn.mpg.de)

Posted in

- Talk [1]

Speaker:

Emiliano Ambrosi
Affiliation:

MPIM
Date:

Tue, 2020-04-07 14:00 - 15:00 Given a family Y------> X of smooth projective varieties over a field k, we study the locus X^{ex} of closed points x in X where the rank of the Neron-Severi group of the fiber of Y------> X at x is bigger then the rank of the generic one. As simple examples show, the properties of X^{ex} depend on the arithmetic of k. We prove that if the characteristic of k is positive and k is infinite finitely generated then this locus is "small", extending previous results in characteristic zero of André and Cadoret-Tamagawa. Since the proof involves a combination of l-adic and p-adic methods, the talk will be an occasion to make an overview on the relations between various p-adic and l-adic cohomology theories in positive characteristic.

**Links:**

[1] https://www.mpim-bonn.mpg.de/taxonomy/term/39

[2] https://www.mpim-bonn.mpg.de/node/3444

[3] https://www.mpim-bonn.mpg.de/node/5312