In Arakelov theory one studies an intersection theory over a hypothetical completion of the spectrum of integers, where arithmetic cycles are equipped with additional analytic data. After a brief introduction to this theory, I will introduce a new notion of irreducibility for arithmetic cycles. While the naive notion of irreducibility turns out to be not very practical, I will show that the new notion allows to prove an analogue of Bertini's theorem. As a by-product, I will present an equidistribution result on the divisors of small sections, which in particular implies a new equidistribution result on the zero sets of integer polynomials.