Cohen-Lenstra heuristics in the presence of roots of unity

Will Sawin (Columbia University)

05-Mar-2021, 16:30-17:30 (3 years ago)

Abstract: The Cohen-Lenstra heuristics predict the distribution of the $\ell$-part of the class group of quadratic fields. Cohen and Martinet generalized them to extensions of an arbitrary base field, however, these are no longer believed to be accurate when the base field contains $\ell$-power roots of unity. In joint work with Michael Lipnowski and Jacob Tsimerman, we give a corrected conjecture for quadratic extensions of a base field with arbitrary roots of unity. This conjecture is motivated by a function-field model, where we prove it is correct in the large $q$ limit of the large genus limit, building on the work of Ellenberg, Venkatesh, and Westerland. Our method involves defining two bilinear invariants on the class group, constructing a "linearization" of the geometric distribution, and comparing it to the actual distribution using moments.

algebraic geometrynumber theory

Audience: researchers in the topic


Séminaire de géométrie arithmétique et motivique (Paris Nord)

Organizers: Farrell Brumley, Olivier Wittenberg*
*contact for this listing

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