Elliptic Curves and Modular Forms in Algebraic Topology Proceedings of a Conference Held at Institute Advanced Stdy (Lecture Notes in Mathematics) by P. S. Landweber

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ISBN 100387194908
ISBN 109780387194905

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: Elliptic Curves and Modular Forms in Algebraic Topology: Proceedings of a Conference held at the Institute for Advanced Study Princeton, Sept.(Lecture Notes in Mathematics) (): Landweber, Peter S.: Books4/5(1).

A small conference was held in September to discuss new applications of elliptic functions and modular forms in algebraic topology, which had led to the introduction of elliptic genera and elliptic cohomology.

The resulting papers range, fom these topics through to quantum field theory, with. The theory of elliptic curves and modular forms provides a fruitful meeting ground for such diverse areas as number theory, complex analysis, algebraic geometry, and representation theory.

This book starts out with a problem from elementary number theory and proceeds to lead its reader into the modern theory, covering such topics as the Hasse Cited by: elliptic curves and modular forms Download elliptic curves and modular forms or read online books in PDF, EPUB, Tuebl, and Mobi Format.

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In mathematics, elliptic cohomology is a cohomology theory in the sense of algebraic is related to elliptic curves and modular forms. History and motivation. Historically, elliptic cohomology arose from the study of elliptic was known by Atiyah and Hirzebruch that if acts smoothly and non-trivially on a spin manifold, then the index of the Dirac operator vanishes.

A small conference was held in September to discuss new applications of elliptic functions and modular forms in algebraic topology, which had led to the. V Elliptic curves and modular forms 1 The Riemann surfacesX 0.N/ analysis, and topology usually taught in ad-vancedundergraduateor beginninggraduatecourses.

Some knowledgeof alge- Throughout the book, kis a field and kal is an algebraic closure of Size: 1MB. Get this from a library. Elliptic curves and modular forms in algebraic topology: proceedings of a conference, held at the Institute for Advanced Study, Princeton, Sept.

[Peter S Landweber; Institute for Advanced Study (Princeton, N.J.);]. This will give you a very solid and rather modern introduction into the subject algebraic curves, and to elliptic curves in particular. Afterwards Elliptic Curves and Modular Forms in Algebraic Topology book 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. Get this from a library. Elliptic curves and modular forms in algebraic topology: proceedings of a conference held at the Institute for Advanced Study, Princeton, Sept.

[P S Landweber;]. Elliptic Curves by J.S. Milne. This note explains the following topics: Plane Curves, Rational Points on Plane Curves, The Group Law on a Cubic Curve, Functions on Algebraic Curves and the Riemann-Roch Theorem, Reduction of an Elliptic Curve Modulo p, Elliptic Curves over Qp, Torsion Points, Neron Models, Elliptic Curves over the Complex Numbers, The Mordell-Weil Theorem: Statement and.

Elliptic Curves and Modular Forms in Algebraic Topology: Proceedings of a Conference Held at the Institute for Advanced Study, Princeton, Sept. | Landweber P. (Ed) | download | B–OK.

Download books for free. Find books. Elliptic Curves And Modular Forms by Robert C. Rhoades File Type: PDF Number of Pages: Description This note is an introduction to elliptic curves and modular forms. These play a central role in modern arithmetical geometry Elliptic Curves and Modular Forms in Algebraic Topology book even in applications to cryptography.

The theory of topological modular forms is an intricate blend of classical algebraic modular forms and stable homotopy groups of spheres. The construction of this theory combines an algebro-geometric perspective on elliptic curves over finite fields with techniques from algebraic topology, particularly stable homotopy theory.

"Elliptic Curves, Modular Forms, and their L-Functions" by Alvaro Lozano-Robledo is maybe the best math book I've ever read.

It's been real hard learning analytic number theory. There aren't many affordable, accessible books for a freshman and you need to know a lot of background information.

An Introduction to the Theory of Elliptic Curves The Discrete Logarithm Problem Fix a group G and an element g 2 Discrete Logarithm Problem (DLP) for G is: Given an element h in the subgroup generated by g, flnd an integer m satisfying h = gm: The smallest integer m satisfying h = gm is called the logarithm (or index) of h with respect to g, and is denotedFile Size: KB.

Request PDF | OnPeter S. Landweber and others published Elliptic cohomology and modular forms | Find, read and cite all the research you need on ResearchGateAuthor: Peter Landweber. Elliptic Curves, Hilbert Modular Forms and Galois Deformations.

The notes by Mladen Dimitrov present the basics of the arithmetic theory of Hilbert modular forms and varieties, with an emphasis on the study of the images of the attached Galois representations, on modularity lifting theorems over totally real number fields, and on the.

Elliptic Curves, Modular Forms and Cryptography: Proceedings of the Advanced Instructional Workshop on Algebraic Number Theory | Ashwani K. Bhandari, D. Nagaraj, B. Modular Functions and Modular Forms (Elliptic Modular Curves) J.S.

Milne Version Ma From topology, we know that there is a simply connected topological space Xz(the universal covering space of X/and a map pWXz!Xwhich is a Affine plane algebraic curves Let kbe a field. An affine plane algebraic curve Cover kis File Size: KB. This book is an introduction to some of these problems, and an overview of the theories used nowadays to attack them, presented so that the number theory is always at the forefront of the discussion.

Lozano-Robledo gives an introductory survey of. A Quick Introduction to Algebraic Geometry and Elliptic Curves 1 D.S. Nagaraj and B. Sury In this volume, there are articles on the following topics in elliptic curves: Mordell-Weil theorem, Nagell-Lutz theorem, Thue’s theorem, Siegel’s theorem, ‘-adic representation attached to an elliptic curve over.

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.

Abstract: Modular forms appear in many facets of mathematics, and have played important roles in geometry, mathematical physics, number theory, representation theory, topology, and other areas. Aroundmotivated by technical issues in homotopy theory, Mark Mahowald, Haynes Miller and I constructed a topological refinement of modular forms, which we call {\em topological Cited by:   Landweber P.S.

() Elliptic cohomology and modular forms. In: Landweber P.S. (eds) Elliptic Curves and Modular Forms in Algebraic Topology. Lecture Notes in Mathematics, vol Cited by: E. Witten, The index of the Dirac operator in loop space, Elliptic Curves and Modular Forms in Algebraic Topology (New York) (P.

Landweber, ed.), Lecture Notes in Mathematics, vol. Author: Michael J. Hopkins. elliptic curves in cryptography. However, even among this cornucopia of literature, I hope that this updated version of the original text will continue to be useful. The past two decades have witnessed tremendous progress in the study of elliptic curves.

Among the many highlights are the proof by Merel [] of uniform bound-Cited by: Online shopping for Algebraic Geometry from a great selection at Books Store. Skip to main Try Prime Elliptic Curves, Modular Forms, and Their L-functions (Student Mathematical Library) 2.

Algebraic Topology 3 December by Allen Hatcher. Paperback. $ used & new. Table of Contents. Front/Back Matter. View this volume's front and back matter; Part I. Chapter 1. Corbett Redden – Elliptic genera and elliptic cohomology Chapter 2.

Carl Mautner – Ellliptic curves and modular forms Chapter 3. The authors present introductory material in algebraic topology from a novel point of view in using a homotopy-theoretic approach. This carefully written book can be read by any student who knows some topology, providing a useful method to quickly learn this novel homotopy-theoretic point of view of algebraic topology.

Modular Forms and Elliptic Curves: Taniyama-Shimura Date: 10/30/97 at From: Daniel Grech Subject: Modular Forms and Elliptic Curves Hi Dr. Math, I watched a PBS show on Fermat's last theorem, and they kept talking about modular forms and elliptic curves and how they are related. This book, authored over a decade ago by UCLA’s Haruzo Hida, should probably be studied in tandem with the same author’s Modular Forms and Galois Cohomology, with this pair of sources then providing sufficient background for the reader to become able to study Andrew Wiles’ work on Fermat’s Lastthe three broad areas that Wiles brought into play to prove the.

The theory of elliptic curves and modular forms is one subject where the most diverse branches of Mathematics like complex analysis, algebraic geometry, representation theory and number theory come together.

Our point of view will be number theoretic. A well-known feature of number theory is theFile Size: KB. textbooks are available on the E-book Directory. Algebra. Differential Forms in Algebraic Topology,Raoul BottLoring W.

Introduction to Elliptic Curves and Author: Kevin de Asis. The theory of elliptic curves and modular forms provides a fruitful meeting ground for such diverse areas as number theory, complex analysis, algebraic geometry, and representation theory.

This book starts out with a problem from elementary number theory and proceeds to lead its reader into the modern theory, covering such topics as the Hasse 4/5(1).

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.

Chapter 1. A historical overview of elliptic cohomology 25 Chapter 2. Elliptic curves and modular forms 39 Chapter 3. The moduli stack of elliptic curves 48 Chapter 4. The Landweber exact functor theorem 58 Chapter 5.

Sheaves in homotopy theory 69 Chapter 6. Bousfield localization and the. Book Title:Introduction to Elliptic Curves and Modular Forms (Graduate Texts in Mathematics) The theory of elliptic curves and modular forms provides a fruitful meeting ground for such diverse areas as number theory, complex analysis, algebraic geometry, and representation theory.

One of the classics on the theory of elliptic curves and modular forms. It gives a nice introduction to the theory od Weierstrass elliptic curves, rational points on elliptic curves, and slightly advanced topics in the theory.

One special aspect of this book is the smooth treatment of the theory of modular forms of half-integer weight/5. a modular curve of the form X 0(N). Any such elliptic curve has the property that its Hasse-Weil zeta function has an analytic continuation and satisfies a functional equation of the standard type.

If an elliptic curve over Qwith a given j-invariant is modular then it is easy to see that all elliptic curves withCited by:. Introduction to Elliptic Curves and Modular Forms by Neal I.

Koblitz,available at Book Depository with free delivery worldwide.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 theory of elliptic curves in its modern formulation, through the use of basic algebraic number theory and algebraic geometry.4/5(9).

We now want to construct the moduli space of elliptic curves. In order to do this we will need to first understand the meaning of the following statement: Over the complex numbers, an elliptic curve is a torus. We have already seen in Elliptic Curves what an elliptic curve looks like when graphed in the – plane, where and are real.

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