Dante Bonolis : 2-torsion in class groups of number fields

In 2020, Bhargava, Shankar, Taniguchi, Thorne, Tsimerman, and Zhao established that, for a given number field $K$ with a degree $n\geq 5$, the size of the $2$-torsion is bounded by $h_{2}(K) \ll D^{\frac{1}{2}-\frac{1}{2n}}$, where $D_{K}$ is the discriminant of $K$ over $\mathbb{Q}$. In this presentation, we will introduce new bounds that take into account the geometry of the lattice underlying the ring of integers of $K$. This research is a joint project with Pierre Le Boudec.

• Category: Number Theory
• Duration: 43:49
• Date:  November 1, 2023 at 3:10 PM
• Views: 94
• Tags:   seminar, Number Theory Seminar