The bad part of the class group

Abstract: The Cohen-Lenstra-Martinet Heuristics provide us with basic ideas on the statistical results class groups of number fields. We can apply the heuristics to the $p$-Sylow subgroups of the class groups when $p$ does not divide the order of the Galois group. In this talk, however, I will first present an algebraic result on the structure of the $p$-Sylow subgroups of the class groups when $p$ divides the Galois group. Then I will show that some of these primes can give us statistical results which show qualitative difference from primes not dividing the order of the Galois group.

number theory

Audience: researchers in the discipline

POINT: New Developments in Number Theory

Series comments: There will be two 20-minute contributed talks during each meeting aimed at a general number theory audience, including graduate students.

Participants are welcome to stay following the talks to have further discussions with the speakers or meet other audience members.

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