Research-Bounds on 2-torsion in class groups of number fields

Research

Algebra & Combinatorics Seminar

Bounds on 2-torsion in class groups of number fields

Speaker: ZHAO Yongqiang (Westlake University)
Time: Jan 16, 2019, 16:00-17:00
Location: Conference Room 415, Hui Yuan 3#

Abstract: A folklore conjecture asserts that for any fixed prime p and integer n, the size of the p-torsion in the class group of a degree n number field is smaller than any power of the discriminant. In all but a few cases, the best known result towards this conjecture is the trivial bound given by the Brauer-Siegel Theorem.

We make progress on this conjecture by giving the first nontrivial bound on the size of the 2-torsion of the class group of any number field in terms of its discriminant. Several applications of this result will also be discussed.