Elliptic Curves And Modular Forms In Algebraic Topology PDF Download
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Author | : Peter S. Landweber |
Publisher | : Springer |
Total Pages | : 232 |
Release | : 2006-11-15 |
Genre | : Mathematics |
ISBN | : 3540393005 |
Download Elliptic Curves and Modular Forms in Algebraic Topology Book in PDF, ePub and Kindle
A small conference was held in September 1986 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 considerable attention to formal groups, homology and cohomology theories, and circle actions on spin manifolds. Ed. Witten's rich article on the index of the Dirac operator in loop space presents a mathematical treatment of his interpretation of elliptic genera in terms of quantum field theory. A short introductory article gives an account of the growth of this area prior to the conference.
Author | : Peter S. Landweber |
Publisher | : |
Total Pages | : 240 |
Release | : 2014-01-15 |
Genre | : |
ISBN | : 9783662203811 |
Download Elliptic Curves and Modular Forms in Algebraic Topology Book in PDF, ePub and Kindle
Author | : Christopher L. Douglas |
Publisher | : American Mathematical Soc. |
Total Pages | : 353 |
Release | : 2014-12-04 |
Genre | : Mathematics |
ISBN | : 1470418843 |
Download Topological Modular Forms Book in PDF, ePub and Kindle
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. It has applications to and connections with manifold topology, number theory, and string theory. This book provides a careful, accessible introduction to topological modular forms. After a brief history and an extended overview of the subject, the book proper commences with an exposition of classical aspects of elliptic cohomology, including background material on elliptic curves and modular forms, a description of the moduli stack of elliptic curves, an explanation of the exact functor theorem for constructing cohomology theories, and an exploration of sheaves in stable homotopy theory. There follows a treatment of more specialized topics, including localization of spectra, the deformation theory of formal groups, and Goerss-Hopkins obstruction theory for multiplicative structures on spectra. The book then proceeds to more advanced material, including discussions of the string orientation, the sheaf of spectra on the moduli stack of elliptic curves, the homotopy of topological modular forms, and an extensive account of the construction of the spectrum of topological modular forms. The book concludes with the three original, pioneering and enormously influential manuscripts on the subject, by Hopkins, Miller, and Mahowald.
Author | : |
Publisher | : |
Total Pages | : 224 |
Release | : 1988 |
Genre | : Algebraic topology |
ISBN | : 9780387194905 |
Download Elliptic Curves and Modular Forms in Algebraic Topology Book in PDF, ePub and Kindle
Author | : Ashwani K. Bhandari |
Publisher | : Springer |
Total Pages | : 339 |
Release | : 2003-07-15 |
Genre | : Mathematics |
ISBN | : 9386279150 |
Download Elliptic Curves, Modular Forms and Cryptography Book in PDF, ePub and Kindle
Author | : |
Publisher | : |
Total Pages | : 224 |
Release | : 1964 |
Genre | : Algebraic topology |
ISBN | : 9780387194905 |
Download Elliptic Curves and Modular Forms in Algebraic Topology Book in PDF, ePub and Kindle
Author | : Winfried Bruns |
Publisher | : |
Total Pages | : 224 |
Release | : 1988 |
Genre | : Algebraic topology |
ISBN | : |
Download Elliptic Curves and Modular Forms in Algebraic Topology Book in PDF, ePub and Kindle
Author | : Haruzo Hida |
Publisher | : World Scientific |
Total Pages | : 375 |
Release | : 2000-09-27 |
Genre | : Mathematics |
ISBN | : 9814492892 |
Download Geometric Modular Forms And Elliptic Curves Book in PDF, ePub and Kindle
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.
Author | : Gary Cornell |
Publisher | : Springer Science & Business Media |
Total Pages | : 608 |
Release | : 1997 |
Genre | : Mathematics |
ISBN | : 9780387946092 |
Download Modular Forms and Fermat’s Last Theorem Book in PDF, ePub and Kindle
A collection of expanded versions of lectures given at an instructional conference on number theory and arithmetic geometry held at Boston University. The purpose of the conference, and indeed this book, is to introduce and explain the many ideas and techniques used by Wiles in his proof, and to explain how his result can be combined with Ribet's theorem and ideas of Frey and Serre to show, at long last, that Fermat's Last Theorem is true. The book begins with an overview of the complete proof, theory of elliptic curves, modular functions, modular curves, Galois cohomology, and finite group schemes. In recognition of the historical significance of Fermat's Last Theorem, the volume concludes by reflecting on the history of the problem, while placing Wiles' theorem into a more general Diophantine context suggesting future applications.
Author | : Jan Hendrik Bruinier |
Publisher | : Springer Science & Business Media |
Total Pages | : 273 |
Release | : 2008-02-10 |
Genre | : Mathematics |
ISBN | : 3540741194 |
Download The 1-2-3 of Modular Forms Book in PDF, ePub and Kindle
This book grew out of three series of lectures given at the summer school on "Modular Forms and their Applications" at the Sophus Lie Conference Center in Nordfjordeid in June 2004. The first series treats the classical one-variable theory of elliptic modular forms. The second series presents the theory of Hilbert modular forms in two variables and Hilbert modular surfaces. The third series gives an introduction to Siegel modular forms and discusses a conjecture by Harder. It also contains Harder's original manuscript with the conjecture. Each part treats a number of beautiful applications.