Number Theory Seminar: On the distribution of class groups — beyond Cohen-Lenstra and Gerth

SEMINARS, NUMBER THEORY

Speaker:

Yuan Liu - University of Illinois Urbana-Champaign

The Cohen-Lenstra heuristic studies the distribution of the p-part of the class group of quadratic number fields for odd prime $p$. Gerth’s conjecture regards the distribution of the $2$-part of the class group of quadratic fields. The main difference between these conjectures is that while the (odd) $p$-part of the class group behaves completely “randomly”, the $2$-part of the class group does not since the $2$-torsion of the class group is controlled by the genus field. In this talk, we will discuss a new conjecture generalizing Cohen-Lenstra and Gerth’s conjectures. The techniques involve Galois cohomology and the embedding problem of global fields.

For more info, see https://ashvin-swaminathan.github.io/home/NTSeminar.html