Divisibility of Selmer groups and class groups

Abstract

In this paper, we study two topics. One is the divisibility problem of class groups of quadratic number fields and its connections to algebraic geometry. The other is the construction of Selmer group and Tate-Shafarevich group for an abelian variety defined over a number field.

21 pages, to appear in Hardy-Ramanujan Journal, comments are welcome, section 2 and 3 in this paper contain a survey of previously submitted preprints arXiv:1906.08233 and arXiv:1903.04210