Titel: Malle's conjecture with multiple invariants
Abstract: Fix a number field K, a finite group G, and a subgroup H. Malle conjecturally predicted the asymptotic number of Galois extensions L of K with Galois group G such that |disc(L^H)| <= X as X goes to infinity. In this talk, we define several invariants inv_1, ..., inv_m of Galois extensions of K with Galois group G and make a conjecture on the asymptotic number of extensions that satisfy 1/2 X_i < inv_i(L) <= X_i for all i as X_1,...,X_m go to infinity. We discuss special cases that are known.