Kato’s Euler system
Kolyvagin’s Theorem I
On the exceptional zeros of p-adic L-functions of Hilbert modular forms
The use of modular symbols to attach p-adic Lfunctions to Hecke eigenforms goes back to the work of Manin et al in the 70s.
The Beilinson-Flach Euler system
In this talk, I will set up the general Euler system machinery of Rubin and look at its properties and examples.
A bounded Beilinson-Flach Euler system for a pair of non-ordinary forms
Building on the previous talk, I will set up the construction of a (flat, sharp) integral Euler system associated to the Rankin-Selberg product for a pair of non-ordinary modular forms and also show the Iwasawa theoretic results one can obtain from the same.
p-adic Asai L-functions for Bianchi modular forms
The Asai (or twisted tensor) L-function attached to a Bianchi modular form is the ‘restriction to the rationals’ of the standard L-function. Introduced by Asai in 1977, subsequent study has linked its special values to the arithmetic of the corresponding form.