Abstract

Iwasawa theory investigates the behavior of Selmer groups and special values of L-functions in p-adic families.

In recent years, the role of the root number (the sign of the functional equation) has become more significant.

For example, after the influential work of Bertolini-Darmon-Prasanna,research on specializations whose root numbers change from +1 to -1 has become popular.

The anticyclotomic family of CM elliptic curves at non-ordinary prime studied by the speaker and collaborators in recent years is a case where root numbers change more wildly (it is a non-trianguline family).

In this talk, we will review the development of Iwasawa theory from the viewpoint of root numbers, and explain the latest results of the speaker and others.

 

Organizer: Ming-Lun Hsieh (NTU)