Abstract
Fix a prime . Let be the Galois representation coming from a non-CM irreducible component of Hida’s -ordinary Hecke algebra. Assume the residual representation is absolutely irreducible. Under a minor technical condition we identify a subring of containing such that the image of is large with respect to . That is, contains for some nonzero -ideal . This paper builds on recent work of Hida who showed that the image of such a Galois representation is large with respect to . Our result is an -adic analogue of the description of the image of the Galois representation attached to a non-CM classical modular form obtained by Ribet and Momose in the 1980s.
Citation
Jaclyn Lang. "On the image of the Galois representation associated to a non-CM Hida family." Algebra Number Theory 10 (1) 155 - 194, 2016. https://doi.org/10.2140/ant.2016.10.155
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