On the irreducibility and distribution of arithmetic divisors

Vendredi, 3. février 2023 - 14:15 - 15:15

Robert Wilms (Université de Bâle)


In arithmetic intersection theory, one studies an analogue of classical intersection theory on varieties over the integers, with additional analytic data playing the role of a hypothetical fiber at infinity. In this talk, I will introduce the notion of epsilon-irreducibility for arithmetic divisors, meaning that the degree of the analytic part is small compared to the degree of the irreducible classical part. I will show an analogue of Bertini's theorem for this notion. Moreover, I will discuss applications of the proof to the study of the distribution of arithmetic divisors. In particular, I will present an equidistribution result for the zero sets of integer polynomials of bounded Bombieri norm.