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Variations on a theorem of Tate /
"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 tak...
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Providence, RI :
American Mathematical Society,
2019.
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| Colección: | Memoirs of the American Mathematical Society ;
no. 1238. |
| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- 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
- 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