Julie Tavernier

University of Bath


Abelian number fields with restricted ramification type and rational points on stacks


Linfoot Number Theory Seminar


12th February 2025, 11:00 am – 12:00 pm
Fry Building, 2.04


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 in terms of sums of Euler products. 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. Finally, I will briefly discuss how this stacky viewpoint can be used to prove a result in the vein of the Malle-Bhargava heuristics via the equidistribution of rational points on BG.





Organisers: Holly Green, Besfort Shala

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