Averages of p-torsion in class groups over function fields---good and bad primes
Recent developments in Analytic Number Theory May 01, 2017 - May 05, 2017
Location: MSRI: Simons Auditorium
Class Field Theory
11R58 - Arithmetic theory of algebraic function fields [See also 14-XX]
When we consider the average size of the p-torsion in class groups of quadratic fields, the behavior for p=2 is controlled by genus theory and is different from the conjectured behavior for odd primes, which is uniform in a certain sense over all odd primes. In this talk, we will consider the question when quadratic fields are replaced by fields of higher degree--for which primes p are the class group averages "bad" versus "good"? We will explain some theorems on class group averages for extensions of function fields that show some subtleties in the classification of good and bad primes
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