Geometric deformations of modular Galois representations
Geometric deformations of modular Galois representations
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模伽罗瓦表示的几何变形
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发表时间：
2004
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通讯作者：
M. Kisin
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作者：
M. Kisin
设f是Γ1（N）上的新形式，Vf是f的二维p-adic Galois表示.设S是包含Np的素因子的有限素数集，用adVf表示Vf的伴随.在对f的适当条件下，证明了H1 g（G_n，S，adVf）= 0.利用这一结果，我们证明了f的剩余表示的泛变形空间在对应于f的点处是光滑的和三维的.当f具有有限斜率时，也可以利用这个结果给出对应于f的点处的Coleman-Mazur“特征曲线”的形变理论描述。
Let f be a newform on Γ1(N), and Vf 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 adVf the adjoint of Vf. Under some mild conditions on f, we show that H1g(Gℚ,S,adVf)=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.