[PDF] The Arithmetic Of Elliptic Curves

The Arithmetic of Elliptic Curves PDF
Author: Joseph H. Silverman
Publisher: Springer Science & Business Media
ISBN: 9780387094946
Size: 44.37 MB
Format: PDF, Kindle
Category : Mathematics
Languages : en
Pages : 513
View: 3739

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The Arithmetic Of Elliptic Curves

by Joseph H. Silverman, release date 2009-04-20, The Arithmetic Of Elliptic Curves Books available in PDF, EPUB, Mobi Format. Download The Arithmetic Of Elliptic Curves books, The theory of elliptic curves is distinguished by its long history and by the diversity of the methods that have been used in its study. This book treats the arithmetic approach in its modern formulation, through the use of basic algebraic number theory and algebraic geometry. Following a brief discussion of the necessary algebro-geometric results, the book proceeds with an exposition of the geometry and the formal group of elliptic curves, elliptic curves over finite fields, the complex numbers, local fields, and global fields. Final chapters deal with integral and rational points, including Siegels theorem and explicit computations for the curve Y = X + DX, while three appendices conclude the whole: Elliptic Curves in Characteristics 2 and 3, Group Cohomology, and an overview of more advanced topics.




[PDF] Advanced Topics In The Arithmetic Of Elliptic Curves

Advanced Topics in the Arithmetic of Elliptic Curves PDF
Author: Joseph H. Silverman
Publisher: Springer Science & Business Media
ISBN: 1461208513
Size: 77.61 MB
Format: PDF, Mobi
Category : Mathematics
Languages : en
Pages : 528
View: 345

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Advanced Topics In The Arithmetic Of Elliptic Curves

by Joseph H. Silverman, release date 2013-12-01, Advanced Topics In The Arithmetic Of Elliptic Curves Books available in PDF, EPUB, Mobi Format. Download Advanced Topics In The Arithmetic Of Elliptic Curves books, In the introduction to the first volume of The Arithmetic of Elliptic Curves (Springer-Verlag, 1986), I observed that "the theory of elliptic curves is rich, varied, and amazingly vast," and as a consequence, "many important topics had to be omitted." I included a brief introduction to ten additional topics as an appendix to the first volume, with the tacit understanding that eventually there might be a second volume containing the details. You are now holding that second volume. it turned out that even those ten topics would not fit Unfortunately, into a single book, so I was forced to make some choices. The following material is covered in this book: I. Elliptic and modular functions for the full modular group. II. Elliptic curves with complex multiplication. III. Elliptic surfaces and specialization theorems. IV. Neron models, Kodaira-Neron classification of special fibers, Tate's algorithm, and Ogg's conductor-discriminant formula. V. Tate's theory of q-curves over p-adic fields. VI. Neron's theory of canonical local height functions.




[PDF] The Arithmetic Of Elliptic Curves

The Arithmetic of Elliptic Curves PDF
Author: Joseph H. Silverman
Publisher: Springer Science & Business Media
ISBN: 1475719205
Size: 20.30 MB
Format: PDF, ePub, Docs
Category : Mathematics
Languages : en
Pages : 402
View: 5401

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The Arithmetic Of Elliptic Curves

by Joseph H. Silverman, release date 2013-03-09, The Arithmetic Of Elliptic Curves Books available in PDF, EPUB, Mobi Format. Download The Arithmetic Of Elliptic Curves books, The theory of elliptic curves is distinguished by its long history and by the diversity of the methods that have been used in its study. This book treats the arithmetic approach in its modern formulation, through the use of basic algebraic number theory and algebraic geometry. Following a brief discussion of the necessary algebro-geometric results, the book proceeds with an exposition of the geometry and the formal group of elliptic curves, elliptic curves over finite fields, the complex numbers, local fields, and global fields. Final chapters deal with integral and rational points, including Siegels theorem and explicit computations for the curve Y = X + DX, while three appendices conclude the whole: Elliptic Curves in Characteristics 2 and 3, Group Cohomology, and an overview of more advanced topics.




[PDF] Arithmetic Moduli Of Elliptic Curves

Arithmetic Moduli of Elliptic Curves PDF
Author: Nicholas M. Katz
Publisher: Princeton University Press
ISBN: 9780691083520
Size: 79.79 MB
Format: PDF, ePub, Mobi
Category : Mathematics
Languages : en
Pages : 514
View: 1037

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Arithmetic Moduli Of Elliptic Curves

by Nicholas M. Katz, release date 1985-02-21, Arithmetic Moduli Of Elliptic Curves Books available in PDF, EPUB, Mobi Format. Download Arithmetic Moduli Of Elliptic Curves books, This work is a comprehensive treatment of recent developments in the study of elliptic curves and their moduli spaces. The arithmetic study of the moduli spaces began with Jacobi's "Fundamenta Nova" in 1829, and the modern theory was erected by Eichler-Shimura, Igusa, and Deligne-Rapoport. In the past decade mathematicians have made further substantial progress in the field. This book gives a complete account of that progress, including not only the work of the authors, but also that of Deligne and Drinfeld.




[PDF] Vorlesungen Ber Allgemeine Funktionentheorie Und Elliptische Funktionen

Vorlesungen   ber allgemeine Funktionentheorie und elliptische Funktionen PDF
Author: Adolf Hurwitz
Publisher:
ISBN:
Size: 71.71 MB
Format: PDF, Docs
Category : Elliptic functions
Languages : de
Pages : 399
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Vorlesungen Ber Allgemeine Funktionentheorie Und Elliptische Funktionen

by Adolf Hurwitz, release date 1922, Vorlesungen Ber Allgemeine Funktionentheorie Und Elliptische Funktionen Books available in PDF, EPUB, Mobi Format. Download Vorlesungen Ber Allgemeine Funktionentheorie Und Elliptische Funktionen books, With an additional article by R. Courant: Geometrische Funktionentheorie.




[PDF] Lectures On The Mordell Weil Theorem

Lectures on the Mordell Weil Theorem PDF
Author: Jean Pierre Serre
Publisher: Springer-Verlag
ISBN: 3663140601
Size: 66.84 MB
Format: PDF, Docs
Category : Mathematics
Languages : en
Pages : 220
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Lectures On The Mordell Weil Theorem

by Jean Pierre Serre, release date 2013-07-02, Lectures On The Mordell Weil Theorem Books available in PDF, EPUB, Mobi Format. Download Lectures On The Mordell Weil Theorem books,




[PDF] Naive Mengenlehre

Naive Mengenlehre PDF
Author: Paul R. Halmos
Publisher: Vandenhoeck & Ruprecht
ISBN: 9783525405277
Size: 16.19 MB
Format: PDF, ePub
Category : Arithmetic
Languages : de
Pages : 132
View: 3859

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Naive Mengenlehre

by Paul R. Halmos, release date 1976, Naive Mengenlehre Books available in PDF, EPUB, Mobi Format. Download Naive Mengenlehre books,




[PDF] Elliptic Curves Over Number Fields With Prescribed Reduction Type

Elliptic Curves over Number Fields with Prescribed Reduction Type PDF
Author: Michael Laska
Publisher: Vieweg + Teubner Verlag
ISBN:
Size: 53.86 MB
Format: PDF, ePub
Category : Mathematics
Languages : en
Pages : 213
View: 4028

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Elliptic Curves Over Number Fields With Prescribed Reduction Type

by Michael Laska, release date 1983, Elliptic Curves Over Number Fields With Prescribed Reduction Type Books available in PDF, EPUB, Mobi Format. Download Elliptic Curves Over Number Fields With Prescribed Reduction Type books, Let K be an algebraic number field. The function attaching to each elliptic curve over K its conductor is constant on isoger. y classes of elliptic curves over K (for the definitions see chapter 1). ~Ioreover, for a given ideal a in OK the number of isogeny classes of elliptic curves over K with conductor a is finite. In these notes we deal with the following problem: How can one explicitly construct a set of representatives for the isogeny classes of elliptic curves over K with conductor a for a given ideal a in OK? The conductor of an elliptic curve over K is a numerical invariant which measures, in some sense, the badness of the reduction of the elliptic curve modulo the prime ideals in OK' It plays an important role in the famous Weil-Langlands conjecture on the connection between elliptic curves over K and congruence subgroups in 5L2(OK) • In case K ~ this connection can be stated as follows. For any ideal a = (N) in ~ let ro(N) be the congruence subgroup ro(N) { (: ~) E 5L2 (~) c E (N) } of 5L2 (~) and let 52 (fo (N» be the space of cusp forms of weight 2 for r 0 (N) Now Weil conjectured that there exists a bijection between the rational normalized eigenforms in 52(ro(N» for the Heckealgebra and the - 2 - Lsug~ny classes uf elliptic curves over ~ with conductor a = (N) .




[PDF] Einf Hrung In Die Kommutative Algebra Und Algebraische Geometrie

Einf  hrung in die kommutative Algebra und algebraische Geometrie PDF
Author: Ernst Kunz
Publisher: Springer-Verlag
ISBN: 3322855260
Size: 79.94 MB
Format: PDF, Mobi
Category : Mathematics
Languages : de
Pages : 239
View: 5527

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Einf Hrung In Die Kommutative Algebra Und Algebraische Geometrie

by Ernst Kunz, release date 2013-03-09, Einf Hrung In Die Kommutative Algebra Und Algebraische Geometrie Books available in PDF, EPUB, Mobi Format. Download Einf Hrung In Die Kommutative Algebra Und Algebraische Geometrie books,