On the irreducibility and distribution of arithmetic divisors
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.