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Geometric Modular Forms and Elliptic Curves.
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...
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Singapore :
World Scientific,
2011.
|
| Edición: | 2nd ed. |
| Temas: | |
| Acceso en línea: | Texto completo |
MARC
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| 049 | |a UAMI | ||
| 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 | ||
| 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 | |
| 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://ebsco.uam.elogim.com/login.aspx?direct=true&scope=site&db=nlebk&AN=457157 |z Texto completo |
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| 938 | |a EBSCOhost |b EBSC |n 457157 | ||
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| 994 | |a 92 |b IZTAP | ||