Last edited by Daijind
Tuesday, May 12, 2020 | History

10 edition of Heegner Modules and Elliptic Curves found in the catalog.

Heegner Modules and Elliptic Curves

by Martin L. Brown

  • 186 Want to read
  • 36 Currently reading

Published by Springer .
Written in English

    Subjects:
  • Algebraic geometry,
  • Science/Mathematics,
  • Homology theory,
  • Mathematics,
  • Geometry - Algebraic,
  • 11F52, 11G05, 11G09, 11G15, 11G40, 11R58,,
  • 14F20, 14G10, 14H52, 14J27, 14K22,
  • Drinfeld Modules,
  • Elliptic Curves,
  • Heegner Points,
  • Mathematics / Number Theory,
  • Tate Conjecture,
  • Tate-Shafarevich Groups,
  • Number Theory,
  • Algebraic fields,
  • Curves, Elliptic

  • Edition Notes

    Lecture Notes in Mathematics

    The Physical Object
    FormatPaperback
    Number of Pages517
    ID Numbers
    Open LibraryOL9832163M
    ISBN 103540222901
    ISBN 109783540222903

    In his seminal paper 'Elliptic modules', V G Drinfeld introduced objects into the arithmetic geometry of global function fields which are nowadays known as 'Drinfeld Modules'. They have many beautiful analogies with elliptic curves and abelian : Hardcover.   Abstract. We discuss the computational application of Heegner points to the study of elliptic curves over Q, concentrating on the curves E d: Dy 2 = x 3 − x arising in the “congruent number” problem. We begin by briefly reviewing the cyclotomic construction of units in real quadratic number fields, which is analogous in many ways to the Heegner-point approach to the arithmetic of Cited by:

    Firstly when k is a global function field of odd characteristic and E is parametrized by a Drinfeld modular curve, and secondly when k is a totally real number field and E/k is parametrized by a Shimura curve. In both cases our approach uses the non-triviality of a sequence of Heegner . Elliptic curves Elliptic curves Definition An elliptic curve over a eld F is a complete algebraic group over F of dimension 1. Equivalently, an elliptic curve is a smooth projective curve of genus one over F equipped with a distinguished F-rational point, the identity element for the algebraic group Size: KB.

    In mathematics, a Heegner point is a point on a modular curve that is the image of a quadratic imaginary point of the upper half-plane. They were defined by Bryan Birch and named after Kurt Heegner, who used similar ideas to prove Gauss's conjecture on imaginary quadratic fields of class number one. After an informal preparatory chapter, the book follows a historical path, beginning with the work of Abel and Gauss on elliptic integrals and elliptic functions. This is followed by chapters on theta functions, modular groups and modular functions, the quintic, the imaginary quadratic field, and on elliptic by:


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Heegner Modules and Elliptic Curves by Martin L. Brown Download PDF EPUB FB2

Buy Heegner Modules and Elliptic Curves (Lecture Notes in Mathematics) on FREE SHIPPING on qualified orders Heegner Modules and Elliptic Curves (Lecture Notes in Mathematics): Martin L. Brown: : BooksCited by: Heegner points on both modular curves and elliptic curves over global fields of any characteristic form the topic of this research monograph.

The Heegner module of an elliptic curve is an original concept introduced in this text. The computation of the cohomology of the Heegner module is Brand: Springer-Verlag Berlin Heidelberg.

Heegner points on both modular curves and elliptic curves over global fields of any characteristic form the topic of this research monograph. The Heegner module of an elliptic curve is an original concept introduced in this text.

Heegner Modules and Elliptic Curves Martin L. Brown (auth.) Heegner points on both modular curves and elliptic curves over global fields of any characteristic form the topic of this research monograph. The Heegner module of an elliptic curve is an original concept introduced in this text. Heegner Modules and Elliptic Curves Heegner points on both modular curves and elliptic curves over global fields of any characteristic form the topic of this research monograph.

The Heegner module of an elliptic curve is an original concept introduced in this text. Heegner Points Let be an elliptic curve defined over with conductor, and fix a modular parametrization. Let be a quadratic imaginary field such that the primes dividing are all unramified and split simplicity, we will also assume be an integral ideal of such and define two elliptic curves over, and since, there is a natural map.

To set the stage for Heegner points, one may compare the state of the theory of elliptic curves over the rationals, E=Q Heegner Modules and Elliptic Curves book short, in the ’s and in the ’s; Serre [15] has already done this, but never mind.

Lest I forget, I should stress that when I say “elliptic curve” I will always mean “elliptic curve Cited by: If is an elliptic curve over a field we let be the ring of all endomorphisms of that are defined over.

Definition (CM Elliptic Curve) An elliptic curve over a subfield of has complex multiplication if. Remark If is an elliptic curve over, then.

This is true even if has complex multiplication. This will give you a very solid and rather modern introduction into the subject algebraic curves, and to elliptic curves in particular. Afterwards you can go back to chaps. II and III and read the theory of schemes and the machinery of sheaf cohomology, if you wish to further pursue algebraic geometry.

From the reviews of the second edition: "Husemöller’s text was and is the great first introduction to the world of elliptic curves and a good guide to the current research literature as well. this second edition builds on the original in several ways.

it has certainly gained a good deal of topicality, appeal, power of inspiration, and educational value for a wider public.5/5(3). Heegner points on both modular curves and elliptic curves over global fields of any characteristic form the topic of this research monograph.

Rating: (not yet rated) 0 with reviews - Be the first. Heegner points on both modular curves and elliptic curves over global fields of any characteristic form the topic of this research monograph.

The main theme of the book is the theory of complex multiplication, Heegner points, and some conjectural variants. The first three chapters introduce the background and prerequisites: elliptic curves, modular forms and the Shimura-Taniyama-Weil conjecture, complex multiplication and the Heegner point construction.

Heegner Modules and Elliptic Curves, Martin L. Brown, Lecture Notes in Mathematics,Springer Stark's Conjectures: Recent Work and New Directions, Ed. David Burns, Christian Popescu, Jonathan Sands, David Solomon, Contemporary MathematicsAMS Preface --Introduction --Preliminaries --Bruhat-Tits trees with complex multiplication --Heegner sheaves --The Heegner module --Cohomology of the Heegner module --Finiteness of the Tate-Shafarevich groups --Appendix A.: Rigid analytic modular forms --Appendix B.: Automorphic forms and elliptic curves over function fields --References --Index.

Cite this chapter as: Brown M.L. () 5. The Heegner module. In: Heegner Modules and Elliptic Curves. Lecture Notes in Mathematics, vol Author: Martin L. Brown. HEEGNER POINTS AND REPRESENTATION THEORY 39 Let x be a Heegner point of conductor c, and let 1 be the standard cusp on X0(N), given by the cyclic isogeny (Gm=qZ.

N Gm=qNZ) of Tate curves over Q. Consider the divisor (x)¡(1) of degree 0, and leta (x)¡(1) be its class in the k-rational points of the Jacobian J0(N).

The finite dimensional rational vector space. Kolyvagin used Heegner points to associate a system of cohomology classes to an elliptic curve over Q and conjectured that the system contains a non-trivial class. His conjecture has profound. Chapter 18 is a brief summary of the modular elliptic curves conjecture and Fermat's Last Theorem from mostly an historical perspective.

The author reviews the material from prior chapters that relate to the modular curve conjecture. The Tate module of an elliptic curve plays a central role. In this setting, a Heegner point of the modular curve XQ(N) is defined as a pair (^j -^ Ej) in which both elliptic curves E¿ have complex multiplication and the rings of.

Heegner Points and the Arithmetic of Elliptic Curves Over Ring Class Extensions1 Robert Bradshaw and William Stein2a,b aGoogle, Seattle bUniversity of Washington Abstract Let Ebe an elliptic curve over Q and let Kbe a quadratic imaginary eld that satis es the Heegner hypothesis.

We study the arithmetic of E over.A Generalized Arithmetic Geometric Mean. This note explains the following topics: Classical arithmetic geometry, The Convergence Theorem, The link with the classical AGM sequence, Point counting on elliptic curves, A theta structure induced by Frobenius.

Author(s): Robert Carls.ties of elliptic curves possessing Weil parametrizations. Any complex multiplication elliptic curve over Q admits a Weil parametrization. Bemark. If E admits a Weil parametrization by X0(N) and if d is a divisor of N which is the product of an even number of distinct primes, and is relatively prime to Njd, then by the work of Eibet and Jacquet.