Statistics for ray class groups of number fields

Alex Bartel (University of Glasgow)

Wednesday 24th March, 2021 16:00-17:00 online (zoom)

Abstract

The Cohen--Lenstra heuristics are a probabilistic model for
class groups of quadratic number fields. I will report on joint work
with Carlo Pagano, in which we generalise these heuristics to ray class
groups. A central role in our heuristics is played by so-called Arakelov
ray class groups. Apart from demonstrating their utility for our
immediate purpose, I will advertise their beauty by re-interpreting a
classical construction that attaches closed geodesics on the quotient of
the hyperbolic upper half plane by SL(2,Z) to (narrow) ideal classes of
real quadratic fields. Only minimal number theoretic background will be
assumed.

 

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