Abstract
We prove potential modularity theorems for $l$-adic representations of any dimension. From these results we deduce the Sato-Tate conjecture for all elliptic curves with nonintegral $j$-invariant defined over a totally real field.
We prove potential modularity theorems for $l$-adic representations of any dimension. From these results we deduce the Sato-Tate conjecture for all elliptic curves with nonintegral $j$-invariant defined over a totally real field.
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