Bernouilli numbers, Eisenstein series and cyclotomic units

Abstract

I will recall what are the objects of the title and explain how one can combine them in a new way to explain a deep Theorem of Mazur and Wiles (proving a conjecture of Iwasawa) that gives a formula for the cardinality of the p-part of the class groups of cyclotomic fields in terms of Bernouilli numbers. "The project leading to this talk has received funding from the European Research Council (ERC)(obriu en una finestra nova) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No 682152): Euler systems and the conjectures of Birch and Swinnerton-Dyer and Block-Kato"