Arithmetic Algebraic Geometry
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Galois Representations And Arithmetic Algebraic Geometry
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Author : Yasutaka Ihara
language : en
Publisher: Kinokuniya Company Limited
Release Date : 1987
Galois Representations And Arithmetic Algebraic Geometry written by Yasutaka Ihara and has been published by Kinokuniya Company Limited this book supported file pdf, txt, epub, kindle and other format this book has been release on 1987 with Mathematics categories.
Algebraic Geometry And Arithmetic Curves
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Author : 刘擎
language : en
Publisher: Oxford Graduate Texts in Mathe
Release Date : 2002
Algebraic Geometry And Arithmetic Curves written by 刘擎 and has been published by Oxford Graduate Texts in Mathe this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002 with Juvenile Nonfiction categories.
Based on the author's course for first-year students this well-written text explains how the tools of algebraic geometry and of number theory can be applied to a study of curves. The book starts by introducing the essential background material and includes 600 exercises.
Conjectures In Arithmetic Algebraic Geometry
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Author : Wilfred W. J. Hulsbergen
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-06-29
Conjectures In Arithmetic Algebraic Geometry written by Wilfred W. J. Hulsbergen and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-06-29 with Technology & Engineering categories.
In this expository text we sketch some interrelations between several famous conjectures in number theory and algebraic geometry that have intrigued math ematicians for a long period of time. Starting from Fermat's Last Theorem one is naturally led to introduce L functions, the main, motivation being the calculation of class numbers. In partic ular, Kummer showed that the class numbers of cyclotomic fields play a decisive role in the corroboration of Fermat's Last Theorem for a large class of exponents. Before Kummer, Dirichlet had already successfully applied his L-functions to the proof of the theorem on arithmetic progressions. Another prominent appearance of an L-function is Riemann's paper where the now famous Riemann Hypothesis was stated. In short, nineteenth century number theory showed that much, if not all, of number theory is reflected by properties of L-functions. Twentieth century number theory, class field theory and algebraic geome try only strengthen the nineteenth century number theorists's view. We just mention the work of E. H~cke, E. Artin, A. Weil and A. Grothendieck with his collaborators. Heeke generalized Dirichlet's L-functions to obtain results on the distribution of primes in number fields. Artin introduced his L-functions as a non-abelian generalization of Dirichlet's L-functions with a generalization of class field theory to non-abelian Galois extensions of number fields in mind.
Arithmetic Geometry And Number Theory
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Author : Lin Weng
language : en
Publisher: World Scientific
Release Date : 2006-06-02
Arithmetic Geometry And Number Theory written by Lin Weng and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-06-02 with Mathematics categories.
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.
Arithmetic Algebraic Geometry
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Author : G., van der Geer
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Arithmetic Algebraic Geometry written by G., van der Geer and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
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. Inspired by these exciting developments, the editors organized a meeting at Texel in 1989 and invited a number of mathematicians to write papers for this volume. Some of these papers were presented at the meeting; others arose from the discussions that took place. They were all chosen for their quality and relevance to the application of algebraic geometry to arithmetic problems. Topics include: arithmetic surfaces, Chjerm functors, modular curves and modular varieties, elliptic curves, Kolyvagin’s work, K-theory and Galois representations. Besides the research papers, there is a letter of Parshin and a paper of Zagier with is interpretations of the Birch-Swinnerton-Dyer Conjecture. 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.
Arithmetic Algebraic Geometry
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Author : Brian David Conrad
language : en
Publisher: American Mathematical Soc.
Release Date :
Arithmetic Algebraic Geometry written by Brian David Conrad and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on with Mathematics categories.
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.
Arithmetic Algebraic Geometry
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Author : G Van Der Geer
language : en
Publisher:
Release Date : 1990-12-01
Arithmetic Algebraic Geometry written by G Van Der Geer and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1990-12-01 with Arithmetical algebraic geometry categories.
Arithmetic Algebraic Geometry
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Author : Jean-Louis Colliot-Thelene
language : en
Publisher: Springer
Release Date : 2006-11-15
Arithmetic Algebraic Geometry written by Jean-Louis Colliot-Thelene and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-15 with Mathematics categories.
This volume contains three long lecture series by J.L. Colliot-Thelene, Kazuya Kato and P. Vojta. Their topics are respectively the connection between algebraic K-theory and the torsion algebraic cycles on an algebraic variety, a new approach to Iwasawa theory for Hasse-Weil L-function, and the applications of arithemetic geometry to Diophantine approximation. They contain many new results at a very advanced level, but also surveys of the state of the art on the subject with complete, detailed profs and a lot of background. Hence they can be useful to readers with very different background and experience. CONTENTS: J.L. Colliot-Thelene: Cycles algebriques de torsion et K-theorie algebrique.- K. Kato: Lectures on the approach to Iwasawa theory for Hasse-Weil L-functions.- P. Vojta: Applications of arithmetic algebraic geometry to diophantine approximations.
Galois Representations In Arithmetic Algebraic Geometry
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Author : A. J. Scholl
language : en
Publisher: Cambridge University Press
Release Date : 1998-11-26
Galois Representations In Arithmetic Algebraic Geometry written by A. J. Scholl and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998-11-26 with Mathematics categories.
Conference proceedings based on the 1996 LMS Durham Symposium 'Galois representations in arithmetic algebraic geometry'.
Arithmetic And Geometry
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Author : Gisbert Wüstholz
language : en
Publisher: Princeton University Press
Release Date : 2019-10-08
Arithmetic And Geometry written by Gisbert Wüstholz and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-10-08 with Mathematics categories.
"Lectures by outstanding scholars on progress made in the past ten years in the most progressive areas of arithmetic and geometry - primarily arithmetic geometry"--