Divisibility of Selmer groups and class groups

Kalyan Banerjee , Kalyan Chakraborty (1) , Azizul Hoque

1 Harish-Chandra Research Institute

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.

Mots clés: Picard group; Class group; Hyperelliptic surface; Imaginary quadratic field; Selmer group; Tate-Shafarevich group; Chow group; Abelian variety 2010

Domaines: Mathématiques [math]; Théorie des nombres [math.NT]

Kalyan Banerjee, Kalyan Chakraborty, Azizul Hoque. Divisibility of Selmer groups and class groups. Hardy-Ramanujan Journal, 2020, Volume 42 - Special Commemorative volume in honour of Alan Baker - 2019, pp.85 - 99. ⟨10.46298/hrj.2020.6460⟩. ⟨hal-02554271⟩