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Description of  Variations on a Theorem of Tate (Memoirs of the American Mathematical Society)

1470435403 pdf Let $F$ be a number field. These notes explore Galois-theoretic, automorphic, and motivic analogues and refinements of Tate's basic result that continuous projective representations $mathrmGal(overlineF/F) to mathrmPGLn(mathbbC)$ lift to $mathrmGLn(mathbbC)$. The author takes special interest in the interaction of this result with algebraicity (for automorphic representations) and geometricity (in the sense of Fontaine-Mazur). On the motivic side, the author studies refinements and generalizations of the classical Kuga-Satake construction. Some auxiliary results touch possible infinity-types of algebraic automorphic representations comparison of the automorphic and Galois Tannakian formalisms'' monodromy (independence-of-$ell$) questions for abstract Galois representations.