×Time: 14.15 on 30 Jan, 2020
Francesco Campagna (University of Copenhagen)
Primes dividing singular moduli
A remarkable property of singular invariants of CM elliptic curves (singular moduli) is that they are always algebraic integers. Hence it makes sense to ask whether, for a fixed set of rational primes S, there exist singular moduli that are S-units. When the set S is empty, Yu. Bilu, P. Habegger and L. Kühne have given a negative answer to the question, proving that singular units do not exist. In this talk we show how the same result holds for the infinite set S of primes congruent to 1 modulo 3 and discuss the more general problem of understanding the prime factorization of singular moduli.