Published on *Max Planck Institute for Mathematics* (http://www.mpim-bonn.mpg.de)

Posted in

- Talk [1]

Speaker:

Tomomi Ozawa
Affiliation:

University Paris 13
Date:

Thu, 2017-11-23 11:10 - 12:00 Measuring congruences among modular forms over arithmetic rings has good applications

to number theory. In particular, Hida has shown in 2013 that the non-existence of the following

two types of congruences is almost equivalent to the vanishing of the $\mu$-invariants of the

Kubota-Leopoldt $p$-adic $L$-function and the Katz anti-cyclotomic $p$-adic $L$-function:

(1) a congruence mod $p$ between a $p$-adic family of Eisenstein series and a non-CM

cuspidal Hida family; (2) a congruence mod $p$ between a non-CM and a CM cuspidal

Hida family. In this talk, I will explain my attempt to describe congruence modules that

classify such types of congruences, in the case where the Hilbert modular forms are defined

over a real quadratic field of narrow ideal class number one.

**Links:**

[1] http://www.mpim-bonn.mpg.de/taxonomy/term/39

[2] http://www.mpim-bonn.mpg.de/node/3444

[3] http://www.mpim-bonn.mpg.de/node/7600