, Volume 157, Issue 2, pp 275-328
Date: 17 Feb 2004

Geometric deformations of modular Galois representations

Rent the article at a discount

Rent now

* Final gross prices may vary according to local VAT.

Get Access

Abstract

Let f be a newform on Γ1(N), and V f the 2-dimensional p-adic Galois representation attached to f. Let S be a finite set of primes containing the primes divisors of Np, and denote by adV f the adjoint of V f . Under some mild conditions on f, we show that H 1 g (G ℚ,S ,adV f )=0.

Using this result, we show that the universal deformation space of the residual representation attached to f is smooth and 3-dimensional at the point corresponding to f. When f has finite slope, one can also use this result to give a deformation theoretic description of the “eigencurve” of Coleman-Mazur at the point corresponding to f.