Elliptic curves, Hilbert modular forms and Galois deformations:
Gespeichert in:
| Format: | Elektronisch E-Book |
|---|---|
| Sprache: | English |
| Veröffentlicht: |
Basel [u.a.]
Springer
2013
|
| Schriftenreihe: | Advanced courses in mathematics
|
| Schlagworte: | |
| Online-Zugang: | BTU01 TUM01 UBA01 UBM01 UBT01 UBW01 UPA01 Volltext Inhaltsverzeichnis Abstract |
| Beschreibung: | 1 Online-Ressource |
| ISBN: | 9783034806176 9783034806183 |
| DOI: | 10.1007/978-3-0348-0618-3 |
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| adam_text | ELLIPTIC CURVES, HILBERT MODULAR FORMS AND GALOIS DEFORMATIONS
/ BERGER, LAURENT
: 2013
TABLE OF CONTENTS / INHALTSVERZEICHNIS
PART I: GALOIS DEFORMATIONS
ON P-ADIC GALOIS REPRESENTATIONS
DEFORMATIONS OF GALOIS REPRESENTATIONS
PART II: HILBERT MODULAR FORMS
ARITHMETIC ASPECTS OF HILBERT MODULAR FORMS AND VARIETIES
EXPLICIT METHODS FOR HILBERT MODULAR FORMS
PART III: ELLIPTIC CURVES
NOTES ON THE PARITY CONJECTURE
DIESES SCHRIFTSTUECK WURDE MASCHINELL ERZEUGT.
ELLIPTIC CURVES, HILBERT MODULAR FORMS AND GALOIS DEFORMATIONS
/ BERGER, LAURENT
: 2013
ABSTRACT / INHALTSTEXT
THE NOTES IN THIS VOLUME CORRESPOND TO ADVANCED COURSES HELD AT THE
CENTRE DE RECERCA MATEMATICA AS PART OF THE RESEARCH PROGRAM IN
ARITHMETIC GEOMETRY IN THE 2009-2010 ACADEMIC YEAR. THE NOTES BY LAURENT
BERGER PROVIDE AN INTRODUCTION TO P-ADIC GALOIS REPRESENTATIONS AND
FONTAINE RINGS, WHICH ARE ESPECIALLY USEFUL FOR DESCRIBING MANY LOCAL
DEFORMATION RINGS AT P THAT ARISE NATURALLY IN GALOIS DEFORMATION
THEORY. THE NOTES BY GEBHARD BOECKLE OFFER A COMPREHENSIVE COURSE ON
GALOIS DEFORMATION THEORY, STARTING FROM THE FOUNDATIONAL RESULTS OF
MAZUR AND DISCUSSING IN DETAIL THE THEORY OF PSEUDO-REPRESENTATIONS AND
THEIR DEFORMATIONS, LOCAL DEFORMATIONS AT PLACES L ≠ P AND LOCAL
DEFORMATIONS AT P WHICH ARE FLAT. IN THE LAST SECTION,THE RESULTS OF
BOECKLE AND KISIN ON PRESENTATIONS OF GLOBAL DEFORMATION RINGS OVER
LOCAL ONES ARE DISCUSSED.THE NOTES BY MLADEN DIMITROV PRESENT THE BASICS
OF THE ARITHMETIC THEORY OF HILBERT MODULAR FORMS AND VARIETIES, WITH AN
EMPHASIS ON THE STUDY OF THE IMAGES OF THE ATTACHED GALOIS
REPRESENTATIONS, ON MODULARITY LIFTING THEOREMS OVER TOTALLY REAL NUMBER
FIELDS, AND ON THE COHOMOLOGY OF HILBERT MODULAR VARIETIES WITH INTEGRAL
COEFFICIENTS. THE NOTES BY LASSINA DEMBELE AND JOHN VOIGHT DESCRIBE
METHODS FOR PERFORMING EXPLICIT COMPUTATIONS IN SPACES OF HILBERT
MODULAR FORMS. THESE METHODS DEPEND ON THE JACQUET-LANGLANDS
CORRESPONDENCE AND ON COMPUTATIONS IN SPACES OF QUATERNIONIC MODULAR
FORMS, BOTH FOR THE CASE OF DEFINITE AND INDEFINITE QUATERNION ALGEBRAS.
SEVERAL EXAMPLES ARE GIVEN, AND APPLICATIONS TO MODULARITY OF GALOIS
REPRESENTATIONS ARE DISCUSSED.THE NOTES BY TIM DOKCHITSER DESCRIBE THE
PROOF, OBTAINED BY THE AUTHOR IN A JOINT PROJECT WITH VLADIMIR
DOKCHITSER, OF THE PARITY CONJECTURE FOR ELLIPTIC CURVES OVER NUMBER
FIELDS UNDER THE ASSUMPTION OF FINITENESS OF THE TATE-SHAFAREVICH GROUP.
THE STATEMENT OF THE BIRCH AND SWINNERTON-DYER CONJECTURE IS INCLUDED,
AS WELL AS A DETAILED STUDY OF LOCAL AND GLOBAL ROOT NUMBERS OF ELLIPTIC
CURVES AND THEIR CLASSIFICATION
DIESES SCHRIFTSTUECK WURDE MASCHINELL ERZEUGT.
|
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| discipline | Mathematik |
| doi_str_mv | 10.1007/978-3-0348-0618-3 |
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| series2 | Advanced courses in mathematics |
| spelling | Elliptic curves, Hilbert modular forms and Galois deformations Laurent Berger ... Basel [u.a.] Springer 2013 1 Online-Ressource txt rdacontent c rdamedia cr rdacarrier Advanced courses in mathematics Galois-Theorie (DE-588)4155901-0 gnd rswk-swf Algebraische Geometrie (DE-588)4001161-6 gnd rswk-swf Zahlentheorie (DE-588)4067277-3 gnd rswk-swf Modulform (DE-588)4128299-1 gnd rswk-swf Algebra (DE-588)4001156-2 gnd rswk-swf Elliptische Kurve (DE-588)4014487-2 gnd rswk-swf Elliptische Kurve (DE-588)4014487-2 s Algebra (DE-588)4001156-2 s Algebraische Geometrie (DE-588)4001161-6 s Zahlentheorie (DE-588)4067277-3 s 1\p DE-604 Modulform (DE-588)4128299-1 s 2\p DE-604 Galois-Theorie (DE-588)4155901-0 s 3\p DE-604 Berger, Laurent 1976- Sonstige (DE-588)141767170 oth https://doi.org/10.1007/978-3-0348-0618-3 Verlag Volltext Springer Fremddatenuebernahme application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=026207012&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Springer Fremddatenuebernahme application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=026207012&sequence=000003&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Abstract 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 3\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Elliptic curves, Hilbert modular forms and Galois deformations Galois-Theorie (DE-588)4155901-0 gnd Algebraische Geometrie (DE-588)4001161-6 gnd Zahlentheorie (DE-588)4067277-3 gnd Modulform (DE-588)4128299-1 gnd Algebra (DE-588)4001156-2 gnd Elliptische Kurve (DE-588)4014487-2 gnd |
| subject_GND | (DE-588)4155901-0 (DE-588)4001161-6 (DE-588)4067277-3 (DE-588)4128299-1 (DE-588)4001156-2 (DE-588)4014487-2 |
| title | Elliptic curves, Hilbert modular forms and Galois deformations |
| title_auth | Elliptic curves, Hilbert modular forms and Galois deformations |
| title_exact_search | Elliptic curves, Hilbert modular forms and Galois deformations |
| title_full | Elliptic curves, Hilbert modular forms and Galois deformations Laurent Berger ... |
| title_fullStr | Elliptic curves, Hilbert modular forms and Galois deformations Laurent Berger ... |
| title_full_unstemmed | Elliptic curves, Hilbert modular forms and Galois deformations Laurent Berger ... |
| title_short | Elliptic curves, Hilbert modular forms and Galois deformations |
| title_sort | elliptic curves hilbert modular forms and galois deformations |
| topic | Galois-Theorie (DE-588)4155901-0 gnd Algebraische Geometrie (DE-588)4001161-6 gnd Zahlentheorie (DE-588)4067277-3 gnd Modulform (DE-588)4128299-1 gnd Algebra (DE-588)4001156-2 gnd Elliptische Kurve (DE-588)4014487-2 gnd |
| topic_facet | Galois-Theorie Algebraische Geometrie Zahlentheorie Modulform Algebra Elliptische Kurve |
| url | https://doi.org/10.1007/978-3-0348-0618-3 http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=026207012&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=026207012&sequence=000003&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT bergerlaurent ellipticcurveshilbertmodularformsandgaloisdeformations |