| Description |
1 online resource (vii, 156 pages) |
| Series |
Memoirs of the American Mathematical Society, 0065-9266 ; volume 258, number 1238 |
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Memoirs of the American Mathematical Society ; no. 1238.
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| Contents |
Cover; Title page; Chapter 1. Introduction; 1.1. Introduction; 1.2. What is assumed of the reader: Background references; 1.3. Acknowledgments; 1.4. Notation; Chapter 2. Foundations & examples; 2.1. Review of lifting results; 2.2. ℓ-adic Hodge theory preliminaries; 2.3. \mr{ }₁; 2.4. Coefficients: Generalizing Weil's CM descent of type Hecke characters; 2.5. W-algebraic representations; 2.6. Further examples: The Hilbert modular case and \mr{ }₂×\mr{ }₂\xrightarrow{⊠}\mr{ }₄; 2.7. Galois lifting: Hilbert modular case; 2.8. Spin examples |
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Chapter 3. Galois and automorphic lifting3.1. Lifting -algebraic representations; 3.2. Galois lifting: The general case; 3.3. Applications: Comparing the automorphic and Galois formalisms; 3.4. Monodromy of abstract Galois representations; Chapter 4. Motivic lifting; 4.1. Motivated cycles: Generalities; 4.2. Motivic lifting: The hyperkähler case; 4.3. Towards a generalized Kuga-Satake theory; Bibliography; Index of symbols; Index of terms and concepts; Back Cover |
| Summary |
"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-l) questions for abstract Galois representations."--Page v |
| Notes |
"March 2019 - Volume 258 - Number 1238 (second of 7 numbers)." |
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"Keywords: Galois representations, algebraic automorphic representations, motives for motivated cycles, monodromy, Kuga-Satake construction, hyperkähler varieties"--Online information |
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Title same as author's dissertation, Princeton University, 2012 |
| Bibliography |
Includes bibliographical references (pages 147-152) and index |
| Notes |
Print version record |
| Subject |
Tate, John Torrence, 1925-2019
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| SUBJECT |
Tate, John Torrence, 1925-2019 fast |
| Subject |
Algebraic number theory.
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Algebraic topology.
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Galois cohomology.
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Galois theory.
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Topología algebraica
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Números, Teoría de
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Algebraic number theory
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Algebraic topology
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Galois cohomology
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Galois theory
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| Form |
Electronic book
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| ISBN |
9781470450670 |
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1470450674 |
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