# Jerusalem Mathematics Colloquium

Thursday, 8th June 2006, 4:00 pm

Mathematics Building, Lecture Hall 2

##

Eknath Ghate

(TATA Institute)

"On the Local Behaviour of Ordinary Galois Representations"

** Abstract:**
Let f be a primitive cusp form of weight at least 2, and let \rho_f be
the p-adic Galois representation attached to f. If f is p-ordinary,
then it is known that the restriction of \rho_f to a decomposition group
at p is `upper triangular'. If in addition f has CM, then this
representation is even `diagonal'.

In this talk we shall provide evidence for the converse. More precisely,
we show that the local Galois representation is not diagonal, for all
except possibly finitely many of the arithmetic members of a non-CM
family of p-ordinary forms. We assume p is odd, and work under some
technical conditions on the residual representation.

We also settle the analogous question for p-ordinary Lambda-adic forms,
under similar conditions. This is joint work with Vinayak Vatsal.

Light refreshments will be served in the faculty lounge at 3:30.

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