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| Softcover ISBN: | 978-1-4704-3540-0 |
| Product Code: | MEMO/258/1238 |
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| MAA Member Price: | $72.90 |
| AMS Member Price: | $48.60 |
| eBook ISBN: | 978-1-4704-5067-0 |
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| Softcover ISBN: | 978-1-4704-3540-0 |
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| Product Code: | MEMO/258/1238.B |
| List Price: | $162.00 $121.50 |
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Book DetailsMemoirs of the American Mathematical SocietyVolume: 258; 2019; 156 ppMSC: Primary 11; 14
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.
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Table of Contents
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Chapters
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1. Introduction
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2. Foundations & examples
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3. Galois and automorphic lifting
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4. Motivic lifting
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Additional Material
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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.
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Chapters
-
1. Introduction
-
2. Foundations & examples
-
3. Galois and automorphic lifting
-
4. Motivic lifting
