Chromatic Selmer groups and arithmetic invariants of elliptic curves

Abstract

Chromatic Selmer groups are modified Selmer groups with local information for supersingular primes p. We sketch their role in establishing the p-primary part of the Birch–Swinnerton-Dyer formula in Sections 2–5, and then study the growth of the Mordell–Weil rank along the Zp-extension of a quadratic imaginary number field in which p splits in Section 6.