1 On the local structure of ordinary Hecke algebras at classical weight one points

摘要

The aim of this chapter is to explain how one can obtain information regarding the membership of a classical weight one eigenform in a Hida family from the geometry of the Eigencurve at the corresponding point. We show, in passing, that all classical members of a Hida family, including those of weight one, share the same local type at all primes dividing the level.