Research from Northwestern University in mathematics provides new insights.(Report)

Journal of Mathematics | March 3, 2009 | Copyright

According to recent research from the United States, "Let K be an arbitrary number field, and let rho : Gal((K) over bar /K) → GL(2)(E) be a nearly ordinary irreducible geometric Galois representation. In this paper, we study the nearly ordinary deformations of rho."

"When K is totally real and rho is modular, results of Hida imply that the nearly ordinary deformation space associated to rho contains a Zariski dense set of points corresponding to 'automorphic' Galois representations. We conjecture that if K is not totally real, then this is never the case, ...

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