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Variations on a Theorem of Tate
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eBook
Variations on a Theorem of Tate
2019
Overview
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
Subject
ISBN
1470435403, 9781470435400
