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Speaker:

Emiliano Ambrosi
Affiliation:

MPIM
Date:

Tue, 07/04/2020 - 14:00 - 15:00
Location:

MPIM Lecture Hall
Parent event:

Seminar on Algebra, Geometry and Physics 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.

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