Seminar series
Date
Thu, 29 May 2025
Time
11:00 -
12:00
Location
C5
Speaker
Jochen Koenigsmann
Organisation
University of Oxford
This is a report on work in progress aiming to prove the conjecture that if the absolute Galois group of a field K is isomorphic to that of \Q then K admits a (possibly trivial) henselian valuation with divisible value group and residue field \Q. What I can prove is that such a field K has a unique ordering and unique p-adic valuations, and that K satisfies Cebotarev's density theorem, Kronecker-Weber, Hasse-Minkowski, quadratic reciprocity etc.
We will show that our conjecture is equivalent to the birational version of Grothendieck's Section Conjecture over \Q, and we will discuss a model theoretic strengthening of our conjecture.