Geometric Modular Forms and Elliptic Curves.

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This book provides a comprehensive account of the theory of moduli spaces of elliptic curves (over integer rings) and its application to modular forms. The construction of Galois representations, which play a fundamental role in Wiles' proof of the Shimura-Taniyama conjecture, is given. In addi...

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Detalles Bibliográficos
Clasificación:Libro Electrónico
Autor principal: Hida, Haruzo
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Singapore : World Scientific, 2011.
Edición:2nd ed.
Temas:
Curves, Elliptic.
Forms, Modular.
Courbes elliptiques.
Formes modulaires.
MATHEMATICS > Geometry > Algebraic.
Curves, Elliptic
Forms, Modular
Acceso en línea:Texto completo

MARC

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100 1 |a Hida, Haruzo. 
245 1 0 |a Geometric Modular Forms and Elliptic Curves. 
250 |a 2nd ed. 
260 |a Singapore :  |b World Scientific,  |c 2011. 
300 |a 1 online resource (468 pages) 
336 |a text  |b txt  |2 rdacontent 
337 |a computer  |b c  |2 rdamedia 
338 |a online resource  |b cr  |2 rdacarrier 
588 0 |a Print version record. 
505 0 |a Preface to the second edition; Preface; Contents; 1. An Algebro-Geometric Tool Box; 1.1 Sheaves; 1.1.1 Sheaves and Presheaves; 1.1.2 Sheafication; 1.1.3 Sheaf Kernel and Cokernel; 1.2 Schemes; 1.2.1 Local Ringed Spaces; 1.2.2 Schemes as Local Ringed Spaces; 1.2.3 Sheaves over Schemes; 1.2.4 Topological Properties of Schemes; 1.3 Projective Schemes; 1.3.1 Graded Rings; 1.3.2 Functor Proj; 1.3.3 Sheaves on Projective Schemes; 1.4 Categories and Functors; 1.4.1 Categories; 1.4.2 Functors; 1.4.3 Schemes as Functors; 1.4.4 Abelian Categories; 1.5 Applications of the Key-Lemma. 
505 8 |a 1.5.1 Sheaf of Differential Forms on Schemes1.5.2 Fiber Products; 1.5.3 Inverse Image of Sheaves; 1.5.4 Affine Schemes; 1.5.5 Morphisms into a Projective Space; 1.6 Group Schemes; 1.6.1 Group Schemes as Functors; 1.6.2 Kernel and Cokernel; 1.6.3 Bialgebras; 1.6.4 Locally Free Groups; 1.6.5 Schematic Representations; 1.7 Cartier Duality; 1.7.1 Duality of Bialgebras; 1.7.2 Duality of Locally Free Groups; 1.8 Quotients by a Group Scheme; 1.8.1 Naive Quotients; 1.8.2 Categorical Quotients; 1.8.3 Geometric Quotients; 1.9 Morphisms; 1.9.1 Topological Definitions; 1.9.2 Diffeo-Geometric Definitions. 
505 8 |a 1.9.3 Applications1.10 Cohomology of Coherent Sheaves; 1.10.1 Coherent Cohomology; 1.10.2 Summary of Known Facts; 1.10.3 Cohomological Dimension; 1.11 Descent; 1.11.1 Covering Data; 1.11.2 Descent Data; 1.11.3 Descent of Schemes; 1.12 Barsotti-Tate Groups; 1.12.1 p-Divisible Abelian Sheaf; Exercise; 1.12.2 Connected- Etale Exact Sequence; 1.12.3 Ordinary Barsotti-Tate Group; 1.13 Formal Scheme; 1.13.1 Open Subschemes as Functors; Exercises; 1.13.2 Examples of Formal Schemes; 1.13.3 Deformation Functors; 1.13.4 Connected Formal Groups; 2. Elliptic Curves; 2.1 Curves and Divisors. 
505 8 |a 2.1.1 Cartier Divisors2.1.2 Serre-Grothendieck Duality; 2.1.3 Riemann-Roch Theorem; 2.1.4 Relative Riemann-Roch Theorem; 2.2 Elliptic Curves; 2.2.1 Definition; 2.2.2 Abel's Theorem; 2.2.3 Holomorphic Differentials; 2.2.4 Taylor Expansion of Differentials; 2.2.5 Weierstrass Equations of Elliptic Curves; 2.2.6 Moduli of Weierstrass Type; 2.3 Geometric Modular Forms of Level 1; 2.3.1 Functorial Definition; 2.3.2 Coarse Moduli Scheme; 2.3.3 Fields of Moduli; 2.4 Elliptic Curves over C; 2.4.1 Topological Fundamental Groups; 2.4.2 Classical Weierstrass Theory; 2.4.3 Complex Modular Forms. 
505 8 |a 2.5 Elliptic Curves over p-Adic Fields2.5.1 Power Series Identities; 2.5.2 Universal Tate Curves; 2.5.3 Etale Covering of Tate Curves; 2.6 Level Structures; 2.6.1 Isogenies; 2.6.2 Level N Moduli Problems; 2.6.3 Generality of Elliptic Curves; 2.6.4 Proof of Theorem 2.6.8; Exercise; 2.6.5 Geometric Modular Forms of Level N; 2.7 L-Functions of Elliptic Curves; 2.7.1 L-Functions over Finite Fields; 2.7.2 Hasse-Weil L-Function; 2.8 Regularity; 2.8.1 Regular Rings; 2.8.2 Regular Moduli Varieties; 2.9 p-Ordinary Moduli Problems; 2.9.1 The Hasse Invariant; 2.9.2 Ordinary Moduli of p-Power Level. 
505 8 |a 2.9.3 Irreducibility of p-Ordinary Moduli. 
520 |a This book provides a comprehensive account of the theory of moduli spaces of elliptic curves (over integer rings) and its application to modular forms. The construction of Galois representations, which play a fundamental role in Wiles' proof of the Shimura-Taniyama conjecture, is given. In addition, the book presents an outline of the proof of diverse modularity results of two-dimensional Galois representations (including that of Wiles), as well as some of the author's new results in that direction. In this new second edition, a detailed description of Barsotti-Tate groups (including formal Li. 
590 |a eBooks on EBSCOhost  |b EBSCO eBook Subscription Academic Collection - Worldwide 
590 |a ProQuest Ebook Central  |b Ebook Central Academic Complete 
650 0 |a Curves, Elliptic. 
650 0 |a Forms, Modular. 
650 6 |a Courbes elliptiques. 
650 6 |a Formes modulaires. 
650 7 |a MATHEMATICS  |x Geometry  |x Algebraic.  |2 bisacsh 
650 7 |a Curves, Elliptic  |2 fast 
650 7 |a Forms, Modular  |2 fast 
758 |i has work:  |a Geometric modular forms and elliptic curves (Text)  |1 https://id.oclc.org/worldcat/entity/E39PCXPY3DWYJmycffJWYVGVfq  |4 https://id.oclc.org/worldcat/ontology/hasWork 
776 0 8 |i Print version:  |a Hida, Haruzo.  |t Geometric Modular Forms and Elliptic Curves.  |d Singapore : World Scientific, ©2011  |z 9789814368643 
856 4 0 |u https://ebookcentral.uam.elogim.com/lib/uam-ebooks/detail.action?docID=919059  |z Texto completo 
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