Variations on a theorem of Tate / Stefan 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 tak...
Saved in:
| Online Access: |
Full Text (via ProQuest) |
|---|---|
| Main Author: | |
| Format: | eBook |
| Language: | English |
| Published: |
Providence, RI :
American Mathematical Society,
2019.
|
| Series: | Memoirs of the American Mathematical Society ;
no. 1238. |
| Subjects: |
MARC
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| 100 | 1 | |a Patrikis, Stefan, |d 1984- |e author. | |
| 245 | 1 | 0 | |a Variations on a theorem of Tate / |c Stefan Patrikis. |
| 264 | 1 | |a Providence, RI : |b American Mathematical Society, |c 2019. | |
| 264 | 4 | |c ©2019. | |
| 300 | |a 1 online resource (vii, 156 pages) | ||
| 336 | |a text |b txt |2 rdacontent. | ||
| 337 | |a computer |b c |2 rdamedia. | ||
| 338 | |a online resource |b cr |2 rdacarrier. | ||
| 490 | 1 | |a Memoirs of the American Mathematical Society, |x 0065-9266 ; |v volume 258, number 1238. | |
| 500 | |a "March 2019 - Volume 258 - Number 1238 (second of 7 numbers)." | ||
| 500 | |a "Keywords: Galois representations, algebraic automorphic representations, motives for motivated cycles, monodromy, Kuga-Satake construction, hyperkähler varieties"--Online information. | ||
| 500 | |a Title same as author's dissertation, Princeton University, 2012. | ||
| 504 | |a Includes bibliographical references (pages 147-152) and index. | ||
| 505 | 0 | |a 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. | |
| 505 | 8 | |a 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. | |
| 520 | |a "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. | ||
| 588 | 0 | |a Print version record. | |
| 600 | 1 | 0 | |a Tate, John Torrence, |d 1925-2019. |
| 650 | 0 | |a Algebraic number theory. | |
| 650 | 0 | |a Algebraic topology. | |
| 650 | 0 | |a Galois cohomology. | |
| 650 | 0 | |a Galois theory. | |
| 600 | 1 | 7 | |a Tate, John Torrence, |d 1925-2019 |2 fast |0 (OCoLC)fst01451401. |
| 650 | 7 | |a Algebraic number theory. |2 fast |0 (OCoLC)fst00804937. | |
| 650 | 7 | |a Algebraic topology. |2 fast |0 (OCoLC)fst00804941. | |
| 650 | 7 | |a Galois cohomology. |2 fast |0 (OCoLC)fst00937323. | |
| 650 | 7 | |a Galois theory. |2 fast |0 (OCoLC)fst00937326. | |
| 776 | 0 | 8 | |i Print version: |a Patrikis, Stefan, 1984- |t Variations on a theorem of Tate. |d Providence, RI : American Mathematical Society, [2019] |z 9781470435400 |w (DLC) 2019013161 |w (OCoLC)1079402472. |
| 830 | 0 | |a Memoirs of the American Mathematical Society ; |v no. 1238. | |
| 856 | 4 | 0 | |u https://ebookcentral.proquest.com/lib/ucb/detail.action?docID=5770284 |z Full Text (via ProQuest) |
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