分野別セミナー

The local Galois representation attached to an ordinary
cuspidal newform of weight two or more is well known
to be reducible. It is even decomposable if the
underlying form has CM.

The non-CM case is more mysterious. In this talk we shall
give examples of non-CM families of ordinary forms for which
every member has a locally reducible but indecomposable Galois
representation (joint work with Vatsal). We shall also
explain a general strategy (developed with Hida) to tackle
the general non-CM case.