Erman Isik: The growth of Tate-Shafarevich groups of p-supersingular elliptic curves over anticyclotomic Zp-extensions at inert primes

Number Theory Seminar: Erman Isik (Bilkent University)

The growth of Tate-Shafarevich groups of p-supersingular elliptic curves over anticyclotomic Zp-extensions at inert primes

In this talk, we will discuss the asymptotic growth of both the Mordell-Weil ranks and the Tate–Shafarevich groups for an elliptic curve E defined over the rational numbers, focusing on its behaviour along the anticyclotomic Zp-extension of an imaginary quadratic K. Here, p is a prime at which E has good supersingular reduction and is inert in K. We will review the definitions and properties of the plus and minus Selmer groups from Iwasawa theory and discuss how these groups can be used to derive arithmetic information about the elliptic curve.