Pierre Le Boudec: 2-torsion in class groups of number fields (NTWS 169)
Channel: Number Theory Web Seminar
Date: 2023-04-27

Abstract: It is well-known that the class number of a number field K of fixed degree n is roughly bounded by the square root of the absolute value of the discriminant of K. However, given a prime number p, the cardinality of the p-torsion subgroup of the class group of K is expected to be much smaller. Unfortunately, beating the trivial bound mentioned above is a hard problem. Indeed, this task had only been achieved for a handful of pairs (n,p) until Bhargava, Shankar, Taniguchi, Thorne, Tsimerman and Zhao managed to do so for any degree n in the case p=2. In this talk we will go through their proof and we will present new bounds which depend on the geometry of the lattice underlying the ring of integers of K. This is joint work with Dante Bonolis. 

Number Theory Web Seminar: https://www.ntwebseminar.org

Original air date: 
Thursday, April 27, 2023 (8am PDT, 11am EDT, 4pm GMT, 5pm CEST, 6pm Israel Daylight Time, 8:30pm Indian Standard Time, 11pm CST)
Friday, April 28, 2023 (1am AEST, 3am NZST)