-- CANCELLED -- Specialization of Néron-Severi groups in positive characteristic

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.