Jiuya Wang, July 2, 2020

Title: Pointwise Bound for ℓ-torsion of Class Groups

Abstract: ℓ-torsion conjecture states that ℓ-torsion of the class group |ClK[ℓ]| for every number field K is bounded by Disc(K)ε. It follows from a classical result of Brauer-Siegel, or even earlier result of Minkowski that the class number |ClK| of a number field K are always bounded by Disc(K)1/2+ε, therefore we obtain a trivial bound Disc(K)1/2+ε on |ClK[ℓ]|. We will talk about results on this conjecture, and recent works on breaking the trivial bound for ℓ-torsion of class groups in some cases based on the work of Ellenberg-Venkatesh.