What kind of prime factorization knowledge will determine a number field?
There is a standard theorem that a Galois number field K is determined by the collection of primes that split completely in K. Trying to generalize this theorem to non-Galois number fields leads to interesting questions about how little or how much of a number field’s splitting law can or cannot determine that field, say, up to isomorphism. In this talk (and possibly another one), we will explore some of these issues.
