Download or read book Icosahedral Galois Representations and Elliptic Curves written by Annette Klute and published by . This book was released on 1996 with total page 116 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Geometric Modular Forms and Elliptic Curves written by Haruzo Hida and published by World Scientific. This book was released on 2000 with total page 382 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Geometric Modular Forms And Elliptic Curves 2nd Edition written by Haruzo Hida and published by World Scientific. This book was released on 2011-12-28 with total page 468 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.In this new second edition, a detailed description of Barsotti-Tate groups (including formal Lie groups) is added to Chapter 1. As an application, a down-to-earth description of formal deformation theory of elliptic curves is incorporated at the end of Chapter 2 (in order to make the proof of regularity of the moduli of elliptic curve more conceptual), and in Chapter 4, though limited to ordinary cases, newly incorporated are Ribet's theorem of full image of modular p-adic Galois representation and its generalization to ‘big’ Λ-adic Galois representations under mild assumptions (a new result of the author). 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).
Download or read book Mod 4 Galois Representations and Elliptic Curves written by Christopher Holden and published by . This book was released on 2008 with total page 90 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Elliptic Curves and Related Topics written by H. Kisilevsky and published by American Mathematical Soc.. This book was released on 1994-01-01 with total page 208 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book represents the proceedings of a workshop on elliptic curves held in St. Adele, Quebec, in February 1992. Containing both expository and research articles on the theory of elliptic curves, this collection covers a range of topics, from Langlands's theory to the algebraic geometry of elliptic curves, from Iwasawa theory to computational aspects of elliptic curves. This book is especially significant in that it covers topics comprising the main ingredients in Andrew Wiles's recent result on Fermat's Last Theorem.
Download or read book Abelian l Adic Representations and Elliptic Curves written by Jean-Pierre Serre and published by CRC Press. This book was released on 1997-11-15 with total page 203 pages. Available in PDF, EPUB and Kindle. Book excerpt: This classic book contains an introduction to systems of l-adic representations, a topic of great importance in number theory and algebraic geometry, as reflected by the spectacular recent developments on the Taniyama-Weil conjecture and Fermat's Last Theorem. The initial chapters are devoted to the Abelian case (complex multiplication), where one
Download or read book Council for African American Researchers in the Mathematical Sciences Volume III written by Council for African American Researchers in the Mathematical Sciences and published by American Mathematical Soc.. This book was released on 2001 with total page 186 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume presents research and expository papers presented at the third and fifth meetings of the Council for African American Researchers in the Mathematical Sciences (CAARMS). The CAARMS is a group dedicated to organizing an annual conference that showcases the current research primarily, but not exclusively, of African Americans in the mathematical sciences, including mathematics, operations research, statistics, and computer science. Held annually since 1995, significant numbers of researchers have presented their current work in hour-long technical presentations, and graduate students have presented their work in organized poster sessions. The events create an ideal forum for mentoring and networking where attendees can meet researchers and graduate students interested in the same fields. For volumes based on previous CAARMS proceedings, see African Americans in Mathematics II (Volume 252 in the AMS series, Contemporary Mathematics), and African Americans in Mathematics (Volume 34 in the AMS series, DIMACS).
Download or read book Arithmetic Algebraic Geometry written by Brian David Conrad and published by American Mathematical Soc.. This book was released on with total page 588 pages. Available in PDF, EPUB and Kindle. Book excerpt: The articles in this volume are expanded versions of lectures delivered at the Graduate Summer School and at the Mentoring Program for Women in Mathematics held at the Institute for Advanced Study/Park City Mathematics Institute. The theme of the program was arithmetic algebraic geometry. The choice of lecture topics was heavily influenced by the recent spectacular work of Wiles on modular elliptic curves and Fermat's Last Theorem. The main emphasis of the articles in the volume is on elliptic curves, Galois representations, and modular forms. One lecture series offers an introduction to these objects. The others discuss selected recent results, current research, and open problems and conjectures. The book would be a suitable text for an advanced graduate topics course in arithmetic algebraic geometry.
Download or read book On Artin s Conjecture for Odd 2 dimensional Representations written by Gerhard Frey and published by Springer. This book was released on 2006-11-15 with total page 160 pages. Available in PDF, EPUB and Kindle. Book excerpt: The main topic of the volume is to develop efficient algorithms by which one can verify Artin's conjecture for odd two-dimensional representations in a fairly wide range. To do this, one has to determine the number of all representations with given Artin conductor and determinant and to compute the dimension of a corresponding space of cusp forms of weight 1 which is done by exploiting the explicit knowledge of the operation of Hecke operators on modular symbols. It is hoped that the algorithms developed in the volume can be of use for many other problems related to modular forms.
Download or read book Hilbert Modular Forms and Iwasawa Theory written by Haruzo Hida and published by Clarendon Press. This book was released on 2006-06-15 with total page 420 pages. Available in PDF, EPUB and Kindle. Book excerpt: The 1995 work of Wiles and Taylor-Wiles opened up a whole new technique in algebraic number theory and, a decade on, the waves caused by this incredibly important work are still being felt. This book, authored by a leading researcher, describes the striking applications that have been found for this technique. In the book, the deformation theoretic techniques of Wiles-Taylor are first generalized to Hilbert modular forms (following Fujiwara's treatment), and some applications found by the author are then discussed. With many exercises and open questions given, this text is ideal for researchers and graduate students entering this research area.
Download or read book Elliptic Curves Hilbert Modular Forms and Galois Deformations written by Laurent Berger and published by Springer Science & Business Media. This book was released on 2013-06-13 with total page 257 pages. Available in PDF, EPUB and Kindle. Book excerpt: The notes in this volume correspond to advanced courses held at the Centre de Recerca Matemàtica as part of the research program in Arithmetic Geometry in the 2009-2010 academic year. The notes by Laurent Berger provide an introduction to p-adic Galois representations and Fontaine rings, which are especially useful for describing many local deformation rings at p that arise naturally in Galois deformation theory. The notes by Gebhard Böckle offer a comprehensive course on Galois deformation theory, starting from the foundational results of Mazur and discussing in detail the theory of pseudo-representations and their deformations, local deformations at places l ≠ p and local deformations at p which are flat. In the last section,the results of Böckle and Kisin on presentations of global deformation rings over local ones are discussed. 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 cohomology of Hilbert modular varieties with integral coefficients. The notes by Lassina Dembélé and John Voight describe methods for performing explicit computations in spaces of Hilbert modular forms. These methods depend on the Jacquet-Langlands correspondence and on computations in spaces of quaternionic modular forms, both for the case of definite and indefinite quaternion algebras. Several examples are given, and applications to modularity of Galois representations are discussed. The notes by Tim Dokchitser describe the proof, obtained by the author in a joint project with Vladimir Dokchitser, of the parity conjecture for elliptic curves over number fields under the assumption of finiteness of the Tate-Shafarevich group. The statement of the Birch and Swinnerton-Dyer conjecture is included, as well as a detailed study of local and global root numbers of elliptic curves and their classification.
Download or read book Arithmetic Geometry Number Theory and Computation written by Jennifer S. Balakrishnan and published by Springer Nature. This book was released on 2022-03-15 with total page 587 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains articles related to the work of the Simons Collaboration “Arithmetic Geometry, Number Theory, and Computation.” The papers present mathematical results and algorithms necessary for the development of large-scale databases like the L-functions and Modular Forms Database (LMFDB). The authors aim to develop systematic tools for analyzing Diophantine properties of curves, surfaces, and abelian varieties over number fields and finite fields. The articles also explore examples important for future research. Specific topics include● algebraic varieties over finite fields● the Chabauty-Coleman method● modular forms● rational points on curves of small genus● S-unit equations and integral points.
Download or read book Modular Curves and Abelian Varieties written by John Cremona and published by Birkhäuser. This book was released on 2012-12-06 with total page 291 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents lectures from a conference on "Modular Curves and Abelian Varieties'' at the Centre de Recerca Matemtica (Bellaterra, Barcelona). The articles in this volume present the latest achievements in this extremely active field and will be of interest both to specialists and to students and researchers. Many contributions focus on generalizations of the Shimura-Taniyama conjecture to varieties such as elliptic Q-curves and Abelian varieties of GL_2-type. The book also includes several key articles in the subject that do not correspond to conference lectures.
Download or read book Proceedings of the Gibbs Symposium written by D. G. Caldi and published by American Mathematical Soc.. This book was released on 1990-11-07 with total page 342 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume, a joint publication with the American Institute of Physics, contains the proceedings of a symposium honoring the memory of Josiah Willard Gibbs, one of the giants of theoretical physics. Three articles provide perspectives on Gibbs, the man, and on the place his work occupies in the history of science. There are also contributions from leading scientists on statistical mechanics, thermodynamics, geophysics, number theory, general relativity, and economics.
Download or read book Zeta Functions in Algebra and Geometry written by Antonio Campillo and published by American Mathematical Soc.. This book was released on 2012 with total page 362 pages. Available in PDF, EPUB and Kindle. Book excerpt: Contains the proceedings of the Second International Workshop on Zeta Functions in Algebra and Geometry held May 3-7, 2010 at the Universitat de les Illes Balears, Palma de Mallorca, Spain. The conference focused on the following topics: arithmetic and geometric aspects of local, topological, and motivic zeta functions, Poincare series of valuations, zeta functions of groups, rings, and representations, prehomogeneous vector spaces and their zeta functions, and height zeta functions.
Download or read book Elementary and Analytic Theory of Algebraic Numbers written by Wladyslaw Narkiewicz and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 712 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book details the classical part of the theory of algebraic number theory, excluding class-field theory and its consequences. Coverage includes: ideal theory in rings of algebraic integers, p-adic fields and their finite extensions, ideles and adeles, zeta-functions, distribution of prime ideals, Abelian fields, the class-number of quadratic fields, and factorization problems. The book also features exercises and a list of open problems.
Download or read book Algebraic Geometry Santa Cruz 1995 written by János Kollár and published by American Mathematical Soc.. This book was released on 1997 with total page 473 pages. Available in PDF, EPUB and Kindle. Book excerpt:
