Date:
Mon, 31/03/202514:30-15:30
Location:
Ross 70
Title: Automorphism groups of field extensions and the minimal ramification problem
Abstract: I will discuss the following problem: given a global field F and finite group G, what is the minimal r such that there exists a finite extension K/F (not necessarily Galois) with Aut(K/F) ≅ G that is ramified over exactly r places of F?
Evidence will be given to the conjecture that the answer is r=0 or 1 for all F, G. An important new tool used in this work is a recent group-theoretic result which says that for any finite group G there exists a natural number n and a subgroup H<S_n of the symmetric group such that N_{S_n}(H)/H ≅ G.
Based on joint work with Cindy Tsang.
Livestream/Recording Link: https://huji.cloud.panopto.eu/Panopto/Pages/Viewer.aspx?id=5672d49a-1bfc-4966-bd3f-b2a900681bde
Abstract: I will discuss the following problem: given a global field F and finite group G, what is the minimal r such that there exists a finite extension K/F (not necessarily Galois) with Aut(K/F) ≅ G that is ramified over exactly r places of F?
Evidence will be given to the conjecture that the answer is r=0 or 1 for all F, G. An important new tool used in this work is a recent group-theoretic result which says that for any finite group G there exists a natural number n and a subgroup H<S_n of the symmetric group such that N_{S_n}(H)/H ≅ G.
Based on joint work with Cindy Tsang.
Livestream/Recording Link: https://huji.cloud.panopto.eu/Panopto/Pages/Viewer.aspx?id=5672d49a-1bfc-4966-bd3f-b2a900681bde