Hilbert modular forms and Iwasawa theory /

Describing the applications found for the Wiles and Taylor technique, this book generalizes the deformation theoretic techniques of Wiles-Taylor to Hilbert modular forms (following Fujiwara's treatment), and also discusses applications found by the author.

Detalles Bibliográficos
Clasificación:Libro Electrónico
Autor principal: Hida, Haruzo (Autor)
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Oxford : Clarendon, 2006.
Colección:Oxford mathematical monographs.
Temas:
Forms, Modular.
Hilbert modular surfaces.
Iwasawa theory.
Formes modulaires.
Surfaces modulaires de Hilbert.
Théorie d'Iwasawa.
MATHEMATICS > Number Theory.
Forms, Modular
Hilbert modular surfaces
Iwasawa theory
Acceso en línea:Texto completo

MARC

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100 1 |a Hida, Haruzo,  |e author. 
245 1 0 |a Hilbert modular forms and Iwasawa theory /  |c Haruzo Hida. 
260 |a Oxford :  |b Clarendon,  |c 2006. 
300 |a 1 online resource (xiv, 402 pages) :  |b illustrations 
336 |a text  |b txt  |2 rdacontent 
337 |a computer  |b c  |2 rdamedia 
338 |a online resource  |b cr  |2 rdacarrier 
347 |a data file 
490 1 |a Oxford mathematical monographs 
504 |a Includes bibliographical references and index. 
520 8 |a Describing the applications found for the Wiles and Taylor technique, this book generalizes the deformation theoretic techniques of Wiles-Taylor to Hilbert modular forms (following Fujiwara's treatment), and also discusses applications found by the author. 
588 0 |a Print version record. 
505 0 |a 1 Introduction; 1.1 Classical Iwasawa theory; 1.1.1 Galois theoretic interpretation of the class group; 1.1.2 The Iwasawa algebra as a deformation ring; 1.1.3 Pseudo-representations; 1.1.4 Two-dimensional universal deformations; 1.2 Selmer groups; 1.2.1 Deligne's rationality conjecture; 1.2.2 Ordinary Galois representations; 1.2.3 Greenberg's Selmer groups; 1.2.4 Selmer groups with general coefficients; 1.3 Deformation and adjoint square Selmer groups; 1.3.1 Nearly ordinary deformation rings; 1.3.2 Adjoint square Selmer groups and differentials 
505 8 |a 2.2.2 Affine algebraic groups2.2.3 Schemes; 2.3 Automorphic forms on quaternion algebras; 2.3.1 Arithmetic quotients; 2.3.2 Archimedean Hilbert modular forms; 2.3.3 Hilbert modular forms with integral coefficients; 2.3.4 Duality and Hecke algebras; 2.3.5 Quaternionic automorphic forms; 2.3.6 The Jacquet-Langlands correspondence; 2.3.7 Local representations of GL(2); 2.3.8 Modular Galois representations; 2.4 The integral Jacquet-Langlands correspondence; 2.4.1 Classical Hecke operators; 2.4.2 Hecke algebras; 2.4.3 Cohomological correspondences; 2.4.4 Eichler-Shimura isomorphisms 
505 8 |a 2.5 Theta series2.5.1 Quaternionic theta series; 2.5.2 Siegel's theta series; 2.5.3 Transformation formulas; 2.5.4 Theta series of imaginary quadratic fields; 2.6 The basis problem of Eichler; 2.6.1 The elliptic Jacquet-Langlands correspondence; 2.6.2 Eichler's integral correspondence; 3 Hecke algebras as Galois deformation rings; 3.1 Hecke algebras; 3.1.1 Automorphic forms on definite quaternions; 3.1.2 Hecke operators; 3.1.3 Inner products; 3.1.4 Ordinary Hecke algebras; 3.1.5 Automorphic forms of higher weight; 3.2 Galois deformation; 3.2.1 Minimal deformation problems 
505 8 |a 3.2.2 Tangent spaces of local deformation functors3.2.3 Taylor-Wiles systems; 3.2.4 Hecke algebras are universal; 3.2.5 Flat deformations; 3.2.6 Freeness over the Hecke algebra; 3.2.7 Hilbert modular basis problems; 3.2.8 Locally cyclotomic deformation; 3.2.9 Locally cyclotomic Hecke algebras; 3.2.10 Global deformation over a p-adic field; 3.3 Base change; 3.3.1 p-Ordinary Jacquet-Langlands correspondence; 3.3.2 Base fields of odd degree; 3.3.3 Automorphic base change; 3.3.4 Galois base change; 3.4 L-invariants of Hilbert modular forms; 3.4.1 Statement of the result 
590 |a ProQuest Ebook Central  |b Ebook Central Academic Complete 
650 0 |a Forms, Modular. 
650 0 |a Hilbert modular surfaces. 
650 0 |a Iwasawa theory. 
650 6 |a Formes modulaires. 
650 6 |a Surfaces modulaires de Hilbert. 
650 6 |a Théorie d'Iwasawa. 
650 7 |a MATHEMATICS  |x Number Theory.  |2 bisacsh 
650 7 |a Forms, Modular  |2 fast 
650 7 |a Hilbert modular surfaces  |2 fast 
650 7 |a Iwasawa theory  |2 fast 
758 |i has work:  |a Hilbert modular forms and Iwasawa theory (Text)  |1 https://id.oclc.org/worldcat/entity/E39PCGrdK9ytmBYHG6WMCFcybd  |4 https://id.oclc.org/worldcat/ontology/hasWork 
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