ncku-talk2022-12-22

Colloquium

DATE 2022-12-22　15:10-16:00

PLACE 數學系館 1F3174教室

SPEAKER 石勝吉博士（University of Vienna）

TITLE On Iwasawa Invariants of Modular forms with Reducible and Non-P-Distinguished Residual Galois Representations

ABSTRACT In this talk, we will first introduce the Iwasawa main conjecture for ordinary modular forms. We will then report a recent joint work with Jun Wang on the p-adic L-functions of p-adic weight one cusp forms f, obtained via the p-stabilization of weight one Eisenstein series E_1(\chi,1). Here \chi is an odd primitive Dirichlet character with \chi(p)=1. As an application, we compute the Iwasawa invariants of ordinary modular forms of weight k>= 2 with the same residual Galois representations as the one of f, which in our setting, is reducible and non-p-distinguished. Combining this with a result of Kato, we prove the Iwasawa main conjecture for these forms.

Colloquium

DATE	2022-12-22　15:10-16:00

PLACE	數學系館 1F3174教室

SPEAKER	石勝吉博士（University of Vienna）

TITLE	On Iwasawa Invariants of Modular forms with Reducible and Non-P-Distinguished Residual Galois Representations

ABSTRACT	In this talk, we will first introduce the Iwasawa main conjecture for ordinary modular forms. We will then report a recent joint work with Jun Wang on the p-adic L-functions of p-adic weight one cusp forms f, obtained via the p-stabilization of weight one Eisenstein series E_1(\chi,1). Here \chi is an odd primitive Dirichlet character with \chi(p)=1. As an application, we compute the Iwasawa invariants of ordinary modular forms of weight k>= 2 with the same residual Galois representations as the one of f, which in our setting, is reducible and non-p-distinguished. Combining this with a result of Kato, we prove the Iwasawa main conjecture for these forms.