Geometric deformations of modular Galois representations
- Mark KisinAffiliated withDepartment of Mathematics, University of Chicago
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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.
- Geometric deformations of modular Galois representations
Volume 157, Issue 2 , pp 275-328
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- Mark Kisin (1)
- Author Affiliations
- 1. Department of Mathematics, University of Chicago, Chicago, IL, 60637, USA