16:00
Abelian number fields with restricted ramification and rational points on stacks
Abstract
A conjecture by Malle gives a prediction for the number of number fields of bounded discriminant. In this talk I will give an asymptotic formula for the number of abelian number fields of bounded height whose ramification type has been restricted to lie in a given subset of the Galois group and provide an explicit formula for the leading constant. I will then describe how counting these number fields can be viewed as a problem of counting rational points on the stack BG and how the existence of such number fields is controlled by a Brauer-Manin obstruction. No prior knowledge of stacks is needed for this talk!
Join Mathematrix on Wednesday November 5th at 2:30 pm in N3.12 for a chill crafts session. We’ll provide some craft materials, or you can bring a current project you are working on. There will be sweet treats and great company.
We are also still actively seeking PhD students to join the Mathematrix Committee. Please email @email if you are interested in helping with Mathematrix now or in future terms.