2019; 156 pp; Softcover
MSC: Primary 11; 14;
Print ISBN: 978-1-4704-3540-0
Product Code: MEMO/258/1238
List Price: $81.00
AMS Member Price: $48.60
MAA Member Price: $72.90
Electronic ISBN: 978-1-4704-5067-0
Product Code: MEMO/258/1238.E
List Price: $81.00
AMS Member Price: $48.60
MAA Member Price: $72.90
Variations on a Theorem of Tate
Share this pageStefan Patrikis
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
Table of Contents
Variations on a Theorem of Tate
- Cover Cover11
- Title page i2
- Chapter 1. Introduction 110
- Chapter 2. Foundations & examples 1928
- 2.1. Review of lifting results 1928
- 2.2. ℓ-adic Hodge theory preliminaries 2534
- 2.3. \mr{𝐺𝐿}₁ 3039
- 2.4. Coefficients: Generalizing Weil’s CM descent of type 𝐴 Hecke characters 3948
- 2.5. W-algebraic representations 4251
- 2.6. Further examples: The Hilbert modular case and \mr{𝐺𝐿}₂×\mr{𝐺𝐿}₂\xrightarrow{⊠}\mr{𝐺𝐿}₄ 4655
- 2.7. Galois lifting: Hilbert modular case 5463
- 2.8. Spin examples 5867
- Chapter 3. Galois and automorphic lifting 6574
- Chapter 4. Motivic lifting 101110
- Bibliography 147156
- Index of symbols 153162
- Index of terms and concepts 155164
- Back Cover Back Cover1170