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...
Saved in:
Online Access: |
Full text (MCPHS users only) |
---|---|
Main Author: | |
Format: | Electronic eBook |
Language: | English |
Published: |
Providence, RI :
American Mathematical Society,
2019
|
Series: | Memoirs of the American Mathematical Society ;
no. 1238. |
Subjects: | |
Local Note: | ProQuest Ebook Central |
MARC
LEADER | 00000cam a2200000 i 4500 | ||
---|---|---|---|
001 | in00000135442 | ||
006 | m o d | ||
007 | cr |n||||||||| | ||
008 | 190410t20192019riu ob 001 0deng d | ||
005 | 20240627010411.7 | ||
020 | |a 9781470450670 | ||
020 | |a 1470450674 | ||
020 | |z 9781470435400 |q (alk. paper) | ||
020 | |z 1470435403 |q (alk. paper) | ||
029 | 1 | |a AU@ |b 000065662836 | |
035 | |a (OCoLC)1096296254 | ||
035 | |a (OCoLC)on1096296254 | ||
040 | |a UIU |b eng |e rda |e pn |c UIU |d OCLCO |d EBLCP |d OCLCF |d COD |d OCLCQ |d OCLCO |d OCLCA |d UAB |d OCL |d OCLCQ |d UKAHL |d OCLCQ |d OCLCO |d OCLCQ |d OCLCO |d OCLCL |d S9M |d OCLCL |d SXB | ||
050 | 4 | |a QA247 |b .P38 2019 | |
082 | 0 | 4 | |a 512.7/4 |2 23 |
100 | 1 | |a Patrikis, Stefan, |d 1984- |e author. |1 https://id.oclc.org/worldcat/entity/E39PCjxPCGKWChdRXCdgXcT8md | |
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. | |
590 | |a ProQuest Ebook Central |b Ebook Central Academic Complete | ||
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. | |
758 | |i has work: |a Variations on a theorem of Tate (Text) |1 https://id.oclc.org/worldcat/entity/E39PCFy4KwfrymfqFPyKMBd8yb |4 https://id.oclc.org/worldcat/ontology/hasWork | ||
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. | |
852 | |b E-Collections |h ProQuest | ||
856 | 4 | 0 | |u https://ebookcentral.proquest.com/lib/mcphs/detail.action?docID=5770284 |z Full text (MCPHS users only) |t 0 |
938 | |a Askews and Holts Library Services |b ASKH |n AH37445243 | ||
938 | |a ProQuest Ebook Central |b EBLB |n EBL5770284 | ||
947 | |a FLO |x pq-ebc-base | ||
999 | f | f | |s 43608be7-84cd-470c-98c1-fe7841f61f85 |i 8832b618-0c58-4881-a87e-e20f272ebcd6 |t 0 |
952 | f | f | |a Massachusetts College of Pharmacy and Health Sciences |b Online |c Online |d E-Collections |t 0 |e ProQuest |h Other scheme |
856 | 4 | 0 | |t 0 |u https://ebookcentral.proquest.com/lib/mcphs/detail.action?docID=5770284 |y Full text (MCPHS users only) |