6 edition of **Modular curves and abelian varieties** found in the catalog.

- 229 Want to read
- 7 Currently reading

Published
**2004** by Birkhäuser Verlag in Boston .

Written in English

- Modular curves,
- Abelian varieties,
- Moduli theory

**Edition Notes**

Includes bibliographical references.

Statement | John Cremona ... [et al.], editors. |

Series | Progress in mathematics ;, v. 224, Progress in mathematics (Boston, Mass.) ;, v. 224. |

Contributions | Cremona, J. E. |

Classifications | |
---|---|

LC Classifications | QA567.2.M63 M63 2004 |

The Physical Object | |

Pagination | p. cm. |

ID Numbers | |

Open Library | OL3301780M |

ISBN 10 | 0817665862, 3764365862 |

LC Control Number | 2004041077 |

In chapter 7 of his book [SH], Shimura computed the zeta function for mod-ular curves and modular abelian varieties by relating the Frobenius morphism with Hecke operators using some congruence relations. We will use some of his ideas to compute the zeta function of the curves that we will deﬂne below. When the mod p representation is. You can look in chapter 8 of Shimura's "Introduction to the arithmetic theory of automorphic forms" or for something a little more modern look at chapter 4 section 2 of Hida's book "Geometric modular forms and elliptic curves. The case k>2 can also be done due to Deligne. $\endgroup$ – sdf Aug 27 '16 at

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It would be difficult to overestimate the influence and importance of modular forms, modular curves, and modular abelian varieties in the development of num- ber theory and arithmetic geometry during the last fifty years. These subjects lie at the heart of many past achievements and future challenges.

For example, the theory of complex Cited by: Modular Curves and Abelian Varieties. Editors (view affiliations) John E. Cremona; Joan-Carles Lario Search within book. Front Matter. Pages i-viii. PDF.

Stable Reduction of Modular Curves Pages On p-adic Families of Automorphic Forms. Kevin Buzzard. Pages ℚ-curves and Abelian Varieties of GL 2-type from Dihedral Genus 2. Modular Curves and Abelian Varieties. Editors: Cremona, J., Lario, J.-C., Quer, J Abelian Varieties over Q and Modular Forms.

Services for this Book. Download Product Flyer Download High-Resolution Cover. Facebook Twitter LinkedIn Google++. Recommended for you. I think the articles and books below are the most important references for learning about modular abelian varieties.

Click on the link for more information about each book. Modular Curves and Modular Forms. Ribet-Stein, Lectures on Serre's Conjectures; Diamond. Stable reduction of modular curves / Irene L. Bouw and Stefan Wewers --On p-adic families of automorphic forms / Kevin Buzzard --Q-curves and abelian varieties of GL[subscript 2]-type from dihedral genus 2 curves / Gabriel Cardona --old subvariety of J[subscript 0](NM) / Janos A.

Csirik --Irreducibility of Galois actions on level 1 Siegel cusp. This book presents lectures from a conference on "Modular Curves and Abelian Varieties'' at the Centre de Recerca Matemàtica (Bellaterra, Barcelona).

The articles in this volume present the latest achievements in this extremely active field and will be of interest both to.

Momose, who was a student of Yasutaka Ihara, made important contributions to the theory of Galois representations attached to modular forms, rational points on elliptic and modular curves, modularity of some families of Abelian varieties, and applications of arithmetic geometry to cryptography.

Abelian varieties appear naturally as Jacobian varieties (the connected components of zero in Picard varieties) and Albanese varieties of other algebraic varieties. The group law of an abelian variety is necessarily commutative and the variety is non-singular.

An elliptic curve is an abelian variety of dimension 1. Abelian varieties have. One of the most intriguing problems of modern number theory is to relate the arithmetic of abelian varieties to the special values of associated L-functions.

A very precise conjecture has been formulated for elliptic curves by Birc~ and Swinnerton-Dyer and generalized to abelian varieties by Tate. The numerical evidence is quite encouraging. • modular curves as Riemann surfaces and as algebraic curves, • Hecke operators and Atkin–Lehner theory, • Hecke eigenforms and their arithmetic properties, • the Jacobians of modular curves and the Abelian varieties associated to Hecke eigenforms, • elliptic and modular curves modulo p and the Eichler–Shimura Relation.

-- Abelian varieties over. and modular forms -- Shimura curves embedded in Igusa\'s threefold -- Shafarevich-Tate groups of nonsquare order.\/span>\"@ en\/a> ; \u00A0\u00A0\u00A0\n schema:description\/a> \" This book presents lectures from a conference on \"Modular Curves and Abelian Varieties\'\' at the Centre de Recerca Matemtica (Bellaterra.

Modular Curves and Abelian Varieties 英文书摘要 It would be difficult to overestimate the influence and importance of Modular forms, Modular curves, and Modular abelian varieties in the development of num ber theory and arithmetic geometry during the last fifty years.

The relation between Q-curves and certain abelian varieties of GL2-type was established by Ribet (‘Abelian varieties over Q and modular forms’, Proceedings of the KAIST Mathematics Workshop. Modular Forms, Hecke Operators, and Modular Abelian Varieties by Kenneth A.

Ribet, William A. Stein. Publisher: University of Washington Number of pages: Description: Contents: The Main objects; Modular representations and algebraic curves; Modular Forms of Level 1; Analytic theory of modular curves; Modular Symbols; Modular Forms of Higher Level; Newforms and Euler Products.

Lecture 2: Abelian varieties The subject of abelian varieties is vast. In these notes we will hit some highlights of the theory, stressing examples and intuition rather than proofs (due to lack of time, among other reasons). We will note analogies with the more concrete case of elliptic curves (as in [Si]), asFile Size: KB.

The theory of moduli spaces of abelian varieties with real multiplication is presented first very explicitly over the complex numbers. Aspects of the general theory are then exposed, in particular, local deformation theory of abelian varieties in positive characteristic.

Though some of the striking developments described above is out of the scope of this introductory book, the author gives a taste of present day research in the area of Number Theory at the very end of the book (giving a good account of modularity theory of abelian ℚ-varieties and ℚ-curves).

Algebraic and Arithmetic Geometry. This note covers the following topics: Rational points on varieties, Heights, Arakelov Geometry, Abelian Varieties, The Brauer-Manin Obstruction, Birational Geomery, Statistics of Rational Points, Zeta functions. Author(s): Caucher Birkar and Tony Feng. Math Modular Abelian Varieties: Almost Complete Notes in Book Form: all: DATE n: TITLE (future lecture titles subject to change) Points on modular curves.

Friday, Sep 6: More about points and genus formulas; Modular symbols. Monday, Sep 7: Modular symbols I. Elliptic Curves This course is an introductory overview of the topic including some of the work leading up to Wiles's proof of the Taniyama conjecture for most elliptic curves and Fermat's Last Theorem.

These notes have been rewritten and published. Abelian Varieties An introduction to both the geometry and the arithmetic of abelian varieties. In Hilbert proposed the generalization of these as the twelfth of his famous problems.

In this book, Goro Shimura provides the most comprehensive generalizations of this type by stating several reciprocity laws in terms of abelian varieties, theta functions, and modular functions of several variables, including Siegel modular functions.

Euler Systems and Arithmetic Geometry. This note explains the following topics: Galois Modules, Discrete Valuation Rings, The Galois Theory of Local Fields, Ramification Groups, Witt Vectors, Projective Limits of Groups of Units of Finite Fields, The Absolute Galois Group of a Local Field, Group Cohomology, Galois Cohomology, Abelian Varieties, Selmer Groups of Abelian Varieties, Kummer.

This book introduces the theory of modular forms with an eye toward the Modularity Theorem:All rational elliptic curves arise from modular forms. The topics covered include • elliptic curves as comple. Indeed, the book is affordable (in fact, the most affordable of all references on the subject), but also a high quality work and a complete introduction to the rich theory of the arithmetic of elliptic curves, with numerous examples and exercises for the reader, many interesting remarks and an updated bibliography.

Abelian varieties and cryptography. In Section 5 we give a brief description of the theory of modular curves o ver C, F or elliptic curves (Abelian varieties of dimension 1). -modular curves as Riemann surfaces and as algebraic curves, -Hecke operators and Atkin-Lehner theory, -Hecke eigenforms and their arithmetic properties, -the Jacobians of modular curves and the Abelian varieties associated to Hecke eigenforms, -elliptic and modular curves modulo p and the Eichler-Shimura Relation,/5(16).

Introduction to Abelian Varieties by V. Kumar Murty,available at Book Depository with free delivery worldwide. One of the most intriguing problems of modern number theory is to relate the arithmetic of abelian varieties to the special values of associated L-functions.

A very precise conjecture has been formulated for elliptic curves by Birc~ and Swinnerton-Dyer and generalized to abelian varieties by Tate. The numerical evidence is quite by: This book gives an introduction to some central results in transcendental number theory with application to periods and special values of modular and hypergeometric functions.

It also includes related results on Calabi–Yau manifolds. Periods of 1-forms on Complex Curves and Abelian Varieties.

Though some of the striking developments described above is out of the scope of this introductory book, the author gives a taste of present day research in the area of Number Theory at the very end of the book (giving a good account of modularity theory of abelian ℚ-varieties and ℚ-curves).Price: $ In mathematics, a Siegel modular variety or Siegel moduli space is an algebraic variety that parametrizes certain types of abelian varieties of a fixed precisely, Siegel modular varieties are the moduli spaces of principally polarized abelian varieties of a fixed dimension.

They are named after Carl Ludwig Siegel, a 20th-century German mathematician who specialized in number theory. This chapter elaborates the moduli of Abelian varieties in positive characteristic.

The interplay between methods in characteristic zero and in positive characteristic has generated an impressive amount of results and new questions. The chapter discusses the theory of Cited by: 4.

TY - BOOK. T1 - Arithmetic compactifications of PEL-type Shimura varieties. AU - Lan, Kai Wen. PY - /3/ Y1 - /3/ N2 - By studying the degeneration of abelian varieties with PEL structures, this book explains the compactifications of smooth integral models of all PEL-type Shimura varieties, providing the logical foundation for several exciting recent by: The topics covered include: elliptic curves as complex tori and as algebraic curves, modular curves as Riemann surfaces and as algebraic curves, Hecke operators and Atkin-Lehner theory, Hecke eigenforms and their arithmetic properties, the Jacobians of modular curves and the Abelian varieties associated to Hecke eigenforms, elliptic and modular.

Abelian varieties are projective algebraic varieties endowed with an Abelian group structure. Over the complex numbers, they can be described as quotients of a vector space by a lattice of full rank.

They are analogs in higher dimensions of elliptic curves, and play an. Introduction to Elliptic Curves and Modular Forms: Edition 2 - Ebook written by Neal I. Koblitz. Read this book using Google Play Books app on your PC, android, iOS devices.

Download for offline reading, highlight, bookmark or take notes while you read Introduction to Elliptic Curves and Modular Forms: Edition 2. In The Moduli Space of Elliptic Curves we discussed how to construct a space whose points correspond to isomorphism classes of elliptic curves space is given by the quotient of the upper half-plane by the special linear group.

Shimura varieties kind of generalize this idea. In some cases their points may correspond to isomorphism classes of abelian varieties over, which are higher. This book introduces the theory of modular forms, from which all rational elliptic curves arise, with an eye toward the Modularity Theorem.

Discussion covers elliptic curves as complex tori and as algebraic curves; modular curves as Riemann surfaces and as algebraic curves; Hecke operators and Atkin-Lehner theory; Hecke eigenforms and their arithmetic properties; the Jacobians of modular.

The book is designed to be accessible to graduate students who have an understanding of schemes and abelian varieties. PEL -type Shimura varieties, which are natural generalizations of modular curves, are useful for studying the arithmetic properties of automorphic forms and automorphic representations, and they have played important roles in.

Pairings occurring in the arithmetic of elliptic curves is available in, or format. This has appeared in Modular Curves and Abelian Varieties, J. Cremona et al., eds., Progress in Math. Basel: Birkhäuser () Proceedings of the conference on arithmetic algebraic geometry, held in.

This book introduces the theory of modular forms with an eye toward the Modularity Theorem: All rational elliptic curves arise from modular forms. The topics covered include * elliptic curves as complex tori and as algebraic curves, * modular curves as Riemann surfaces and as algebraic curves, * Hecke operators and Atkin--Lehner theory, * Hecke eigenforms and their arithmetic properties, * the.

Modularity of Abelian QVarieties Abelian F-varieties of GL(2)-type Endomorphism Algebras of Abelian F-varieties Application to Abelian Q-Varieties Abelian Varieties with Real Multiplication Bibliography List of Symbols Statement Index Index Price: $Q&A for professional mathematicians.

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