LIFTING TORSION GALOIS REPRESENTATIONS

被引:3
作者
Khare, Chandrashekhar [1 ]
Ramakrishna, Ravi [2 ]
机构
[1] Univ Calif Los Angeles, Dept Math, Los Angeles, CA 90095 USA
[2] Cornell Univ, Dept Math, Ithaca, NY 14853 USA
关键词
D O I
10.1017/fms.2015.17
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
Let p >= 5 be a prime, and let O be the ring of integers of a finite extension K of Q(p) with uniformizer pi. Let rho(n) : G(Q) -> GL(2) (O/(pi(n))) have modular mod-pi reduction (rho) over bar, be ordinary at p, and satisfy some mild technical conditions. We show that rho(n) can be lifted to an O-valued characteristic-zero geometric representation which arises from a newform. This is new in the case when K is a ramified extension of Q(p). We also show that a prescribed ramified complete discrete valuation ring O is the weight-2 deformation ring for (rho) over bar for a suitable choice of auxiliary level. This implies that the field of Fourier coefficients of newforms of weight 2, square-free level, and trivial nebentype that give rise to semistable (rho) over bar of weight 2 can have arbitrarily large ramification index at p.
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页数:37
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