Cuspidal-overconvergent Eisenstein series of weight one and the p-adic eigencurve.
The p-stabilization of certain Eisenstein weight one forms are cuspidal-overconvergent forms, and they belong to the cuspidal locus of the p-adic eigencurve.
The Elliptic Stark Conjecture I
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.
The Elliptic Stark Conjecture II
Ichino formula for definite quaternion algebras
p-adic Hodge theory
Ramification of the Eigencurve at classical RM points
J.Bellaïche and M.Dimitrov have shown that the p-adic eigencurve is smooth but not étale over the weight space at p-regular theta series attached to a character of a real quadratic field F in which p splits.
p-adic modular forms over unitary Shimura curves
We study some p-adic properties of modular forms over unitary Shimura curves, including a description of their relation with automorphic representations via p-adic Hodge theory, overconvergence and classicality, and p-adic families.