Session S09 - Number Theory in the Americas

Thursday, July 15, 14:30 ~ 15:00 UTC-3

Some recent development on the Iwasawa theory of fine Selmer groups

Antonio Lei

U. Laval, Canada   -   This email address is being protected from spambots. You need JavaScript enabled to view it.

In Iwasawa theory, we are interested in the asymptotic behaviour of arithmetic objects over a tower of extensions. In the early 2000's, Coates and Sujatha initiated the studies of the Iwasawa theory of the fine Selmer group of an elliptic curve. Fine Selmer groups have the advantage that many arithmetic properties at a fixed prime are independent of the reduction type of the elliptic curve, giving rise to uniform results that resemble those in classical Iwasawa Theory. In this talk, we will discuss some of these properties and recent results on certain relations between fine Selmer groups and the growth of Mordell-Weil ranks of an elliptic curve.

View abstract PDF