Abelian number fields with restricted ramification and rational points on stacks

Date(s)
Wednesday 26th February 2025 (14:00-15:00)
Contact
Event Convenor Contact: Hamid.Abban@nottingham.ac.uk

Description
Speaker's Name: Julie Tavernier
Speaker's Affiliation: University of Bath
Speaker's Research Theme(s): Pure Mathematics,
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.

Venue: Physics C05

School of Mathematical Sciences

The University of Nottingham
University Park
Nottingham, NG7 2RD

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