MARC details
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04225nam a22005415i 4500 |
| 001 - CONTROL NUMBER |
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978-3-0348-0618-3 |
| 003 - CONTROL NUMBER IDENTIFIER |
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DE-He213 |
| 005 - DATE AND TIME OF LATEST TRANSACTION |
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20180115171555.0 |
| 007 - PHYSICAL DESCRIPTION FIXED FIELD--GENERAL INFORMATION |
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cr nn 008mamaa |
| 008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION |
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130614s2013 sz | s |||| 0|eng d |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER |
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| International Standard Book Number |
9783034806183 |
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978-3-0348-0618-3 |
| 024 7# - OTHER STANDARD IDENTIFIER |
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| Standard number or code |
10.1007/978-3-0348-0618-3 |
| Source of number or code |
doi |
| 050 #4 - LIBRARY OF CONGRESS CALL NUMBER |
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| Classification number |
QA241-247.5 |
| 072 #7 - SUBJECT CATEGORY CODE |
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| Subject category code |
PBH |
| Source |
bicssc |
| 072 #7 - SUBJECT CATEGORY CODE |
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| Subject category code |
MAT022000 |
| Source |
bisacsh |
| 082 04 - DEWEY DECIMAL CLASSIFICATION NUMBER |
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| Classification number |
512.7 |
| Edition number |
23 |
| 100 1# - MAIN ENTRY--PERSONAL NAME |
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| Personal name |
Berger, Laurent. |
| Relator term |
author. |
| 245 10 - TITLE STATEMENT |
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| Title |
Elliptic Curves, Hilbert Modular Forms and Galois Deformations |
| Medium |
[electronic resource] / |
| Statement of responsibility, etc. |
by Laurent Berger, Gebhard Böckle, Lassina Dembélé, Mladen Dimitrov, Tim Dokchitser, John Voight. |
| 264 #1 - PRODUCTION, PUBLICATION, DISTRIBUTION, MANUFACTURE, AND COPYRIGHT NOTICE |
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| Place of production, publication, distribution, manufacture |
Basel : |
| Name of producer, publisher, distributor, manufacturer |
Springer Basel : |
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Imprint: Birkhäuser, |
| Date of production, publication, distribution, manufacture, or copyright notice |
2013. |
| 300 ## - PHYSICAL DESCRIPTION |
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| Extent |
XII, 249 p. 11 illus., 2 illus. in color. |
| Other physical details |
online resource. |
| 336 ## - CONTENT TYPE |
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| Content type term |
text |
| Content type code |
txt |
| Source |
rdacontent |
| 337 ## - MEDIA TYPE |
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| Media type term |
computer |
| Media type code |
c |
| Source |
rdamedia |
| 338 ## - CARRIER TYPE |
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| Carrier type term |
online resource |
| Carrier type code |
cr |
| Source |
rdacarrier |
| 347 ## - DIGITAL FILE CHARACTERISTICS |
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| File type |
text file |
| Encoding format |
PDF |
| Source |
rda |
| 490 1# - SERIES STATEMENT |
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| Series statement |
Advanced Courses in Mathematics - CRM Barcelona |
| 505 0# - FORMATTED CONTENTS NOTE |
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| Formatted contents note |
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. |
| 520 ## - SUMMARY, ETC. |
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| Summary, etc. |
The notes in this volume correspond to advanced courses held at the Centre de Recerca Matemàtica 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 Böckle 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 Böckle 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 Dembélé 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. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name as entry element |
Mathematics. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name as entry element |
Algebra. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name as entry element |
Algebraic geometry. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name as entry element |
Number theory. |
| 650 14 - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name as entry element |
Mathematics. |
| 650 24 - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name as entry element |
Number Theory. |
| 650 24 - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name as entry element |
Algebraic Geometry. |
| 650 24 - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name as entry element |
Algebra. |
| 700 1# - ADDED ENTRY--PERSONAL NAME |
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| Personal name |
Böckle, Gebhard. |
| Relator term |
author. |
| 700 1# - ADDED ENTRY--PERSONAL NAME |
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| Personal name |
Dembélé, Lassina. |
| Relator term |
author. |
| 700 1# - ADDED ENTRY--PERSONAL NAME |
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| Personal name |
Dimitrov, Mladen. |
| Relator term |
author. |
| 700 1# - ADDED ENTRY--PERSONAL NAME |
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| Personal name |
Dokchitser, Tim. |
| Relator term |
author. |
| 700 1# - ADDED ENTRY--PERSONAL NAME |
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| Personal name |
Voight, John. |
| Relator term |
author. |
| 710 2# - ADDED ENTRY--CORPORATE NAME |
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| Corporate name or jurisdiction name as entry element |
SpringerLink (Online service) |
| 773 0# - HOST ITEM ENTRY |
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| Title |
Springer eBooks |
| 776 08 - ADDITIONAL PHYSICAL FORM ENTRY |
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| Relationship information |
Printed edition: |
| International Standard Book Number |
9783034806176 |
| 830 #0 - SERIES ADDED ENTRY--UNIFORM TITLE |
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| Uniform title |
Advanced Courses in Mathematics - CRM Barcelona |
| 856 40 - ELECTRONIC LOCATION AND ACCESS |
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| Uniform Resource Identifier |
<a href="http://dx.doi.org/10.1007/978-3-0348-0618-3">http://dx.doi.org/10.1007/978-3-0348-0618-3</a> |
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ZDB-2-SMA |