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Graduate Student Colloquium

Date:
-
Location:
745 Patterson Office Tower
Speaker(s) / Presenter(s):
Robert Cass, University of Kentucky

Title:  Galois theory over the p-adic numbers

Abstract:  The inverse Galois problem asks whether every finite group appears as the Galois group of some finite Galois extension of the rational numbers. One can ask the same question for other fields. In this talk, we will discuss Galois theory over the p-adic numbers. We will see that ramification groups provide a useful tool for analyzing the structure of these Galois groups. Using ramification groups, we will find limitations on the finite groups which can occur as Galois groups over the p-adic numbers.  A review of the necessary facts about the p-adic numbers will be included. This talk is meant to be accessible to anyone with a basic understanding of Galois theory over the rationals.