Variations on a theorem of Tate
Author(s)
Bibliographic Information
Variations on a theorem of Tate
（Memoirs of the American Mathematical Society, no.1238）
American Mathematical Society, 2019
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Includes bibliographical references and indexes
"March 2019, volume 258, number 1238 (second of 7 numbers)"
Description and Table of Contents
Description
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.
Table of Contents
Introduction
Foundations & examples
Galois and automorphic lifting
Motivic lifting
Bibliography
Index of symbols
Index of terms and concepts.
by "Nielsen BookData"