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Author : Yasutaka Ihara
Publisher : Kinokuniya Company Limited
ISBN 13 :
Total Pages : 394 pages
Book Rating : 4.:/5 (5 download)
Download or read book Galois Representations and Arithmetic Algebraic Geometry written by Yasutaka Ihara and published by Kinokuniya Company Limited. This book was released on 1987 with total page 394 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : A. J. Scholl
Publisher : Cambridge University Press
ISBN 13 : 0521644194
Total Pages : 506 pages
Book Rating : 4.5/5 (216 download)
Download or read book Galois Representations in Arithmetic Algebraic Geometry written by A. J. Scholl and published by Cambridge University Press. This book was released on 1998-11-26 with total page 506 pages. Available in PDF, EPUB and Kindle. Book excerpt: Conference proceedings based on the 1996 LMS Durham Symposium 'Galois representations in arithmetic algebraic geometry'.
Author : Scholl/Taylor
Publisher :
ISBN 13 : 9781107048560
Total Pages : 493 pages
Book Rating : 4.0/5 (485 download)
Download or read book Galois Representations in Arithmetic Algebraic Geometry written by Scholl/Taylor and published by . This book was released on 1999 with total page 493 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Yasutaka Ihara
Publisher :
ISBN 13 : 9784864970709
Total Pages : pages
Book Rating : 4.9/5 (77 download)
Download or read book Galois Representations and Arithmetic Algebraic Geometry written by Yasutaka Ihara and published by . This book was released on 2018 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Brian David Conrad
Publisher : American Mathematical Soc.
ISBN 13 : 9780821886915
Total Pages : 588 pages
Book Rating : 4.8/5 (869 download)
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.
Author : G., van der Geer
Publisher : Springer Science & Business Media
ISBN 13 : 1461204577
Total Pages : 450 pages
Book Rating : 4.4/5 (612 download)
Download or read book Arithmetic Algebraic Geometry written by G., van der Geer and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 450 pages. Available in PDF, EPUB and Kindle. Book excerpt: Arithmetic algebraic geometry is in a fascinating stage of growth, providing a rich variety of applications of new tools to both old and new problems. Representative of these recent developments is the notion of Arakelov geometry, a way of "completing" a variety over the ring of integers of a number field by adding fibres over the Archimedean places. Another is the appearance of the relations between arithmetic geometry and Nevanlinna theory, or more precisely between diophantine approximation theory and the value distribution theory of holomorphic maps. Research mathematicians and graduate students in algebraic geometry and number theory will find a valuable and lively view of the field in this state-of-the-art selection.
Author : Bas Edixhoven
Publisher : Princeton University Press
ISBN 13 : 0691142017
Total Pages : 438 pages
Book Rating : 4.6/5 (911 download)
Download or read book Computational Aspects of Modular Forms and Galois Representations written by Bas Edixhoven and published by Princeton University Press. This book was released on 2011-06-20 with total page 438 pages. Available in PDF, EPUB and Kindle. Book excerpt: Modular forms are tremendously important in various areas of mathematics, from number theory and algebraic geometry to combinatorics and lattices. Their Fourier coefficients, with Ramanujan's tau-function as a typical example, have deep arithmetic significance. Prior to this book, the fastest known algorithms for computing these Fourier coefficients took exponential time, except in some special cases. The case of elliptic curves (Schoof's algorithm) was at the birth of elliptic curve cryptography around 1985. This book gives an algorithm for computing coefficients of modular forms of level one in polynomial time. For example, Ramanujan's tau of a prime number p can be computed in time bounded by a fixed power of the logarithm of p. Such fast computation of Fourier coefficients is itself based on the main result of the book: the computation, in polynomial time, of Galois representations over finite fields attached to modular forms by the Langlands program. Because these Galois representations typically have a nonsolvable image, this result is a major step forward from explicit class field theory, and it could be described as the start of the explicit Langlands program. The computation of the Galois representations uses their realization, following Shimura and Deligne, in the torsion subgroup of Jacobian varieties of modular curves. The main challenge is then to perform the necessary computations in time polynomial in the dimension of these highly nonlinear algebraic varieties. Exact computations involving systems of polynomial equations in many variables take exponential time. This is avoided by numerical approximations with a precision that suffices to derive exact results from them. Bounds for the required precision--in other words, bounds for the height of the rational numbers that describe the Galois representation to be computed--are obtained from Arakelov theory. Two types of approximations are treated: one using complex uniformization and another one using geometry over finite fields. The book begins with a concise and concrete introduction that makes its accessible to readers without an extensive background in arithmetic geometry. And the book includes a chapter that describes actual computations.
Author : Dino Lorenzini
Publisher : American Mathematical Society
ISBN 13 : 1470467259
Total Pages : 397 pages
Book Rating : 4.4/5 (74 download)
Download or read book An Invitation to Arithmetic Geometry written by Dino Lorenzini and published by American Mathematical Society. This book was released on 2021-12-23 with total page 397 pages. Available in PDF, EPUB and Kindle. Book excerpt: Extremely carefully written, masterfully thought out, and skillfully arranged introduction … to the arithmetic of algebraic curves, on the one hand, and to the algebro-geometric aspects of number theory, on the other hand. … an excellent guide for beginners in arithmetic geometry, just as an interesting reference and methodical inspiration for teachers of the subject … a highly welcome addition to the existing literature. —Zentralblatt MATH The interaction between number theory and algebraic geometry has been especially fruitful. In this volume, the author gives a unified presentation of some of the basic tools and concepts in number theory, commutative algebra, and algebraic geometry, and for the first time in a book at this level, brings out the deep analogies between them. The geometric viewpoint is stressed throughout the book. Extensive examples are given to illustrate each new concept, and many interesting exercises are given at the end of each chapter. Most of the important results in the one-dimensional case are proved, including Bombieri's proof of the Riemann Hypothesis for curves over a finite field. While the book is not intended to be an introduction to schemes, the author indicates how many of the geometric notions introduced in the book relate to schemes, which will aid the reader who goes to the next level of this rich subject.
Author : Jean-Pierre Serre
Publisher : CRC Press
ISBN 13 : 1439863865
Total Pages : 203 pages
Book Rating : 4.4/5 (398 download)
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
Author : Fred Diamond
Publisher : Cambridge University Press
ISBN 13 : 1316062333
Total Pages : 385 pages
Book Rating : 4.3/5 (16 download)
Download or read book Automorphic Forms and Galois Representations: Volume 1 written by Fred Diamond and published by Cambridge University Press. This book was released on 2014-10-16 with total page 385 pages. Available in PDF, EPUB and Kindle. Book excerpt: Automorphic forms and Galois representations have played a central role in the development of modern number theory, with the former coming to prominence via the celebrated Langlands program and Wiles' proof of Fermat's Last Theorem. This two-volume collection arose from the 94th LMS-EPSRC Durham Symposium on 'Automorphic Forms and Galois Representations' in July 2011, the aim of which was to explore recent developments in this area. The expository articles and research papers across the two volumes reflect recent interest in p-adic methods in number theory and representation theory, as well as recent progress on topics from anabelian geometry to p-adic Hodge theory and the Langlands program. The topics covered in volume one include the Shafarevich Conjecture, effective local Langlands correspondence, p-adic L-functions, the fundamental lemma, and other topics of contemporary interest.
Author : Laurent Berger
Publisher : Springer Science & Business Media
ISBN 13 : 3034806183
Total Pages : 257 pages
Book Rating : 4.0/5 (348 download)
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.
Author : Peter Schneider
Publisher : Cambridge University Press
ISBN 13 : 110718858X
Total Pages : 157 pages
Book Rating : 4.1/5 (71 download)
Download or read book Galois Representations and (Phi, Gamma)-Modules written by Peter Schneider and published by Cambridge University Press. This book was released on 2017-04-20 with total page 157 pages. Available in PDF, EPUB and Kindle. Book excerpt: A detailed and self-contained introduction to a key part of local number theory, ideal for graduate students and researchers.
Author : Joël Bellaïche
Publisher : Springer Nature
ISBN 13 : 3030772632
Total Pages : 319 pages
Book Rating : 4.0/5 (37 download)
Download or read book The Eigenbook written by Joël Bellaïche and published by Springer Nature. This book was released on 2021-08-11 with total page 319 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book discusses the p-adic modular forms, the eigencurve that parameterize them, and the p-adic L-functions one can associate to them. These theories and their generalizations to automorphic forms for group of higher ranks are of fundamental importance in number theory. For graduate students and newcomers to this field, the book provides a solid introduction to this highly active area of research. For experts, it will offer the convenience of collecting into one place foundational definitions and theorems with complete and self-contained proofs. Written in an engaging and educational style, the book also includes exercises and provides their solution.
Author : Lin Weng
Publisher : World Scientific
ISBN 13 : 981256814X
Total Pages : 414 pages
Book Rating : 4.8/5 (125 download)
Download or read book Arithmetic Geometry and Number Theory written by Lin Weng and published by World Scientific. This book was released on 2006 with total page 414 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematics is very much a part of our culture; and this invaluable collection serves the purpose of developing the branches involved, popularizing the existing theories and guiding our future explorations.More precisely, the goal is to bring the reader to the frontier of current developments in arithmetic geometry and number theory through the works of Deninger-Werner in vector bundles on curves over p-adic fields; of Jiang on local gamma factors in automorphic representations; of Weng on Deligne pairings and Takhtajan-Zograf metrics; of Yoshida on CM-periods; of Yu on transcendence of special values of zetas over finite fields. In addition, the lecture notes presented by Weng at the University of Toronto from October to November 2005 explain basic ideas and the reasons (not just the language and conclusions) behind Langlands' fundamental, yet notably difficult, works on the Eisenstein series and spectral decompositions.And finally, a brand new concept by Weng called the Geometric Arithmetic program that uses algebraic and/or analytic methods, based on geometric considerations, to develop the promising and yet to be cultivated land of global arithmetic that includes non-abelian Class Field Theory, Riemann Hypothesis and non-abelian Zeta and L Functions, etc.
Author : Régine Douady
Publisher : Springer Nature
ISBN 13 : 3030327965
Total Pages : 462 pages
Book Rating : 4.0/5 (33 download)
Download or read book Algebra and Galois Theories written by Régine Douady and published by Springer Nature. This book was released on 2020-07-13 with total page 462 pages. Available in PDF, EPUB and Kindle. Book excerpt: Galois theory has such close analogies with the theory of coverings that algebraists use a geometric language to speak of field extensions, while topologists speak of "Galois coverings". This book endeavors to develop these theories in a parallel way, starting with that of coverings, which better allows the reader to make images. The authors chose a plan that emphasizes this parallelism. The intention is to allow to transfer to the algebraic framework of Galois theory the geometric intuition that one can have in the context of coverings. This book is aimed at graduate students and mathematicians curious about a non-exclusively algebraic view of Galois theory.
Author : John William Scott Cassels
Publisher : Cambridge University Press
ISBN 13 : 9780521425308
Total Pages : 148 pages
Book Rating : 4.4/5 (253 download)
Download or read book LMSST: 24 Lectures on Elliptic Curves written by John William Scott Cassels and published by Cambridge University Press. This book was released on 1991-11-21 with total page 148 pages. Available in PDF, EPUB and Kindle. Book excerpt: A self-contained introductory text for beginning graduate students that is contemporary in approach without ignoring historical matters.
Author : Michel Waldschmidt
Publisher : American Mathematical Soc.
ISBN 13 : 0821806068
Total Pages : 410 pages
Book Rating : 4.8/5 (218 download)
Download or read book Number Theory written by Michel Waldschmidt and published by American Mathematical Soc.. This book was released on 1998 with total page 410 pages. Available in PDF, EPUB and Kindle. Book excerpt: To observe the tenth anniversary of the founding of the Ramanujan Mathematical Society, an international conference on Discrete Mathematics and Number Theory was held in January 1996 in Tiruchirapalli, India. This volume contains proceedings from the number theory component of that conference. Papers are divided into four groups: arithmetic algebraic geometry, automorphic forms, elementary and analytic number theory, and transcendental number theory. This work deals with recent progress in current aspects of number theory and covers a wide variety of topics.
