Eisenstein cohomology for GLn and the special values of Rankin-Selberg L-functions:
Introduction -- The cohomology of GLn -- Analytic tools -- Boundary cohomology -- The strongly inner spectrum and applications -- Eisenstein cohomology -- L-functions -- Harish-Chandra modules over Z / by Günter Harder -- Archimedean intertwining operator / by Uwe Weselmann
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Princeton ; Oxford
Princeton University Press
2020
|
| Schriftenreihe: | Annals of mathematics studies
Number 203 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Zusammenfassung: | Introduction -- The cohomology of GLn -- Analytic tools -- Boundary cohomology -- The strongly inner spectrum and applications -- Eisenstein cohomology -- L-functions -- Harish-Chandra modules over Z / by Günter Harder -- Archimedean intertwining operator / by Uwe Weselmann "This monograph, which is intended for the Annals of Math Studies, presents an important new result that lies at the intersection of number theory, geometry, and representation theory. Accordingly, the book will serve as a key reference in these fields. Given its comprehensive methodological approach, the book will also provide a model for future work in these areas. This monograph builds on over forty years of ambitious research, initiated by Günter Harder in 1975. The results presented in this book extend well beyond previous research in the field, and are readily generalizeable"-- |
| Beschreibung: | Includes bibliographical references and index |
| Beschreibung: | xi, 220 Seiten Illustrationen |
| ISBN: | 9780691197883 9780691197890 |
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| 490 | 1 | |a Annals of mathematics studies |v Number 203 | |
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Datensatz im Suchindex
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|---|---|
| adam_text | Eisenstein Cohomology for GLjv
and the Special Values of
Rankin-Selberg L-Functions
Günter Harder
A Raghuram
PRINCETON UNIVERSITY PRESS
PRINCETON AND OXFORD
2020
Universitäts- und
Landesbibliothek
Darmstadt
Contents
Preface ix
1 Introduction 1
1 1 The general context 3
1 2 Strongly inner cohomology and applications 4
1 3 The main theorem on Eisenstein cohomology 7
1 4 The main theorem on arithmetic of Rankin-Selberg L-functions 8
1 5 Some general remarks 10
2 The Cohomology of GLn 12
2 1 The adelic locally symmetric space __ 12
2 2 Highest weight modules A4 jmd the sheaves M 14
2 3 Cohomology of the sheaves M 21
2 4 Integral cohomology 25
3 Analytic Tools 28
3 1 Cuspidal parameters and the representation O* at infinity 28
3 2 Square-integrable cohomology 34
3 3 Cuspidal cohomology 37
4 Boundary Cohomology 40
41A spectral sequence converging to boundary cohomology 40
4 2 Cohomology of dpSa as an induced representation 42
4 3 Cuspidal spectrum versus residual spectrum 46
5 The Strongly Inner Spectrum and Applications 51
5 1 The strongly inner spectrum: definition and properties 51
5 2 Definition of the relative periods 54
5 3 The strongly inner cohomology of the boundary 60
6 Eisenstein Cohomology 71
6 1 Poincare duality and maximal isotropic subspace of boundary
cohomology 71
6 2 The main result on rank-one Eisenstein cohomology 73
63A theorem of Langlands: the constant term of an Eisenstein series 75
CONTENTS
7 L-Functions
7 1 Motivic and cohomological L-functions
7 2 Critical points for L-functions and the combinatorial lemma
7 3 The main result on special values of L-functions
7 4 Some remarks
8 Harish-Chandra Modules over 2 (by Günter Harder)
8 1 Introduction
8 2 Harish-Chandra modules over Z
8 3 First examples
8 4 Induction of Harish-Chandra modules
9 The Archimedean Intertwining Operator (by Uwe Weselmann)
9 1 The general setting
9 2 The intertwining operators
9 3 /-admissible permutations
9 4 Representations and L-functions
9 5 The main theorem on archimedean intertwining operator
9 6 Applications to cohomology
Bibliography
84
84
92
107
119
126
126
128
132
143
168
169
171
179
181
186
199
211
Index
|
| any_adam_object | 1 |
| author | Harder, Günter 1938- Raghuram, A. |
| author_GND | (DE-588)1011622483 (DE-588)1132154081 |
| author_facet | Harder, Günter 1938- Raghuram, A. |
| author_role | aut aut |
| author_sort | Harder, Günter 1938- |
| author_variant | g h gh a r ar |
| building | Verbundindex |
| bvnumber | BV046410333 |
| callnumber-first | Q - Science |
| callnumber-label | QA242 |
| callnumber-raw | QA242.5 |
| callnumber-search | QA242.5 |
| callnumber-sort | QA 3242.5 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SI 830 |
| ctrlnum | (OCoLC)1140165597 (DE-599)KXP1678506680 |
| dewey-full | 514/.23 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 514 - Topology |
| dewey-raw | 514/.23 |
| dewey-search | 514/.23 |
| dewey-sort | 3514 223 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV046410333 |
| illustrated | Illustrated |
| indexdate | 2024-07-10T08:43:53Z |
| institution | BVB |
| isbn | 9780691197883 9780691197890 |
| language | English |
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| physical | xi, 220 Seiten Illustrationen |
| publishDate | 2020 |
| publishDateSearch | 2020 |
| publishDateSort | 2020 |
| publisher | Princeton University Press |
| record_format | marc |
| series | Annals of mathematics studies |
| series2 | Annals of mathematics studies |
| spelling | Harder, Günter 1938- Verfasser (DE-588)1011622483 aut Eisenstein cohomology for GLn and the special values of Rankin-Selberg L-functions Günter Harder, A. Raghuram Princeton ; Oxford Princeton University Press 2020 xi, 220 Seiten Illustrationen txt rdacontent n rdamedia nc rdacarrier Annals of mathematics studies Number 203 Includes bibliographical references and index Introduction -- The cohomology of GLn -- Analytic tools -- Boundary cohomology -- The strongly inner spectrum and applications -- Eisenstein cohomology -- L-functions -- Harish-Chandra modules over Z / by Günter Harder -- Archimedean intertwining operator / by Uwe Weselmann "This monograph, which is intended for the Annals of Math Studies, presents an important new result that lies at the intersection of number theory, geometry, and representation theory. Accordingly, the book will serve as a key reference in these fields. Given its comprehensive methodological approach, the book will also provide a model for future work in these areas. This monograph builds on over forty years of ambitious research, initiated by Günter Harder in 1975. The results presented in this book extend well beyond previous research in the field, and are readily generalizeable"-- Shimura varieties Cohomology operations Number theory Arithmetic groups L-functions Raghuram, A. Verfasser (DE-588)1132154081 aut Erscheint auch als Online-Ausgabe 978-0-691-19793-7 Annals of mathematics studies Number 203 (DE-604)BV000000991 203 HEBIS Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=031822961&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Harder, Günter 1938- Raghuram, A. Eisenstein cohomology for GLn and the special values of Rankin-Selberg L-functions Annals of mathematics studies |
| title | Eisenstein cohomology for GLn and the special values of Rankin-Selberg L-functions |
| title_auth | Eisenstein cohomology for GLn and the special values of Rankin-Selberg L-functions |
| title_exact_search | Eisenstein cohomology for GLn and the special values of Rankin-Selberg L-functions |
| title_full | Eisenstein cohomology for GLn and the special values of Rankin-Selberg L-functions Günter Harder, A. Raghuram |
| title_fullStr | Eisenstein cohomology for GLn and the special values of Rankin-Selberg L-functions Günter Harder, A. Raghuram |
| title_full_unstemmed | Eisenstein cohomology for GLn and the special values of Rankin-Selberg L-functions Günter Harder, A. Raghuram |
| title_short | Eisenstein cohomology for GLn and the special values of Rankin-Selberg L-functions |
| title_sort | eisenstein cohomology for gln and the special values of rankin selberg l functions |
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