The leading constant in Malle’s conjecture

Tim Santens (KU Leuven/University of Bath)

Wednesday 28th February 16:00-17:00 Maths 110

Abstract

Malle has conjectured the order of growth of the number of field extensions with a certain Galois closure of bounded discriminant, but he did not provide a conjecture for the leading constant. Manin made a very similar prediction on the number of point of bounded height on varieties and Peyre gave a conjectural formula for the leading. In this talk I will discuss joint work with Loughran where we give a prediction for the leading constant in Malle’s conjecture in analogy with Peyre’s constant for Manin’s conjecture, based on the analogy that Malle’s conjecture is Manin’s conjecture for certain stacks.

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