Holdings: Elliptic curves, Hilbert modular forms and Galois deformations

Elliptic curves, Hilbert modular forms and Galois deformations:

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Bibliographic Details
Format:	Electronic eBook
Language:	English
Published:	Basel [u.a.] Springer 2013
Series:	Advanced courses in mathematics
Subjects:	Galois-Theorie Algebraische Geometrie Zahlentheorie Modulform Algebra Elliptische Kurve
Online Access:	BTU01 TUM01 UBA01 UBM01 UBT01 UBW01 UPA01 Volltext Inhaltsverzeichnis Abstract
Physical Description:	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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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

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