# Variations on a Theorem of Tate - Memoirs of the American Mathematical Society (Paperback)

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Paperback 156 Pages / Published: 30/05/2019
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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 $\mathrm{Gal}(\overline{F}/F) \to \mathrm{PGL}_n(\mathbb{C})$ lift to $\mathrm{GL}_n(\mathbb{C})$. 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 on: possible infinity-types of algebraic automorphic representations; comparison of the automorphic and Galois Tannakian formalisms'' monodromy (independence-of-$\ell$) questions for abstract Galois representations.

Publisher: American Mathematical Society
ISBN: 9781470435400
Number of pages: 156
Dimensions: 254 x 178 mm

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