Selmer groups of elliptic curves encodes various aspects of the arithmetic of elliptic curves. In this talk, we will discuss a duality result for Selmer groups, over a p-adic Lie extension of a number field. This duality result can be thought of as an algebraic functional equation.

This talk is based on joint works with T. Ochiai and G. Zabradi.

Introductory reading:

1. Introduction to Iwasawa Theory of elliptic curves, Notes by. Ralph Greenberg: http://www.fields.utoronto.ca/sites/default/files/uploads/Introduction-I...

2. The following paper by Perrin-Riou: Groupes de Selmer et Accouplements; Cas Particulier des Courbes Elliptiques (French): http://www.fields.utoronto.ca/sites/default/files/uploads/perrin-riou.dm...

3. Iwasawa theory for p-adic representations by Ralph Greenberg. Algebraic number theory, 97–137, Adv. Stud. Pure Math., 17, Academic Press, Boston, MA, 1989.