Wilhelm Killing Kolloquium: Prof. Dr. Jochen Koenigsmann (University of Oxford) in person: Encoding arithmetic in Galois groups
Thursday, 07.07.2022 16:30 im Raum M2
In the footsteps of Galois, we shall try to recover arithmetic properties from Galois theoretic data.
In particular, we shall analyse what arithmetic information about a field K is encoded in its absolute Galois group G(K),
i.e., the Galois group of a separable closure of K over K.
This is the universal Galois group over K in the sense that every other Galois group over K is a quotient of G(K).
It is by now well known that for real closed or p-adically closed fields, G(K) "knows everything" about the arithmetic of K.
More recently, it was established that if K is the field of rational numbers, then G(K) knows "almost everything" -
we shall make this precise and indicate main steps for the proof during the talk.