Number Theory Seminar
Lilian Pierce
Duke University
Class numbers and p-torsion in class groups of number fields
Abstract: Each number field has a positive integer associated to it called the class number, defined to be the cardinality of the class group of the field. Class numbers are important objects that arise naturally in many contexts in number theory: for example, Gauss famously investigated class numbers of quadratic fields, in the context of classifying the representation of integers by binary quadratic forms. Today, many deep open questions remain about the structure of class groups and the growth and divisibility properties of class numbers as fields vary over an appropriate infinite family. This talk will focus on the size of the p-torsion subgroup of the class group: it is conjectured that for any number field and any rational prime p, the p-torsion part of the class group of the field should be very small, in a suitable sense, relative to the discriminant of the field. This talk will present recent progress on bounding p-torsion in class groups of number fields of degree 2, 3, 4, 5.
Please note special day and time.
Thursday October 13, 2016 at 10:00 AM in SEO 427