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Author: Stephen S. Shatz
Publisher: Princeton University Press
ISBN: 9780691080178
Category : Mathematics
Languages : en
Pages : 268
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Book Description
This volume reproduces, in the first five chapters, the content of a one semester course given at the University of Pennsylvania in the spring of 1968. The final chapter was material that was not presented during the course due to lack of time. The aim of the course was to acquaint students with a body of material upon which some of the modern research in Diophantine geometry and higher arithmetic is based, and in a way which emphasized the many interesting roads out of these elementary foundations.
Author: Stephen S. Shatz
Publisher: Princeton University Press
ISBN: 9780691080178
Category : Mathematics
Languages : en
Pages : 268
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Book Description
This volume reproduces, in the first five chapters, the content of a one semester course given at the University of Pennsylvania in the spring of 1968. The final chapter was material that was not presented during the course due to lack of time. The aim of the course was to acquaint students with a body of material upon which some of the modern research in Diophantine geometry and higher arithmetic is based, and in a way which emphasized the many interesting roads out of these elementary foundations.
Author: Stephen S. Shatz
Publisher: Princeton University Press
ISBN: 1400881854
Category : Mathematics
Languages : en
Pages : 265
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Book Description
In this volume, the author covers profinite groups and their cohomology, Galois cohomology, and local class field theory, and concludes with a treatment of duality. His objective is to present effectively that body of material upon which all modern research in Diophantine geometry and higher arithmetic is based, and to do so in a manner that emphasizes the many interesting lines of inquiry leading from these foundations.
Author: Pierre Dèbes
Publisher: Springer Science & Business Media
ISBN: 3034804873
Category : Mathematics
Languages : en
Pages : 411
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Book Description
This Lecture Notes volume is the fruit of two research-level summer schools jointly organized by the GTEM node at Lille University and the team of Galatasaray University (Istanbul): "Geometry and Arithmetic of Moduli Spaces of Coverings (2008)" and "Geometry and Arithmetic around Galois Theory (2009)". The volume focuses on geometric methods in Galois theory. The choice of the editors is to provide a complete and comprehensive account of modern points of view on Galois theory and related moduli problems, using stacks, gerbes and groupoids. It contains lecture notes on étale fundamental group and fundamental group scheme, and moduli stacks of curves and covers. Research articles complete the collection.
Author: Michael D. Fried
Publisher: Springer Science & Business Media
ISBN: 9783540228110
Category : Computers
Languages : en
Pages : 812
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Book Description
Field Arithmetic explores Diophantine fields through their absolute Galois groups. This largely self-contained treatment starts with techniques from algebraic geometry, number theory, and profinite groups. Graduate students can effectively learn generalizations of finite field ideas. We use Haar measure on the absolute Galois group to replace counting arguments. New Chebotarev density variants interpret diophantine properties. Here we have the only complete treatment of Galois stratifications, used by Denef and Loeser, et al, to study Chow motives of Diophantine statements. Progress from the first edition starts by characterizing the finite-field like P(seudo)A(lgebraically)C(losed) fields. We once believed PAC fields were rare. Now we know they include valuable Galois extensions of the rationals that present its absolute Galois group through known groups. PAC fields have projective absolute Galois group. Those that are Hilbertian are characterized by this group being pro-free. These last decade results are tools for studying fields by their relation to those with projective absolute group. There are still mysterious problems to guide a new generation: Is the solvable closure of the rationals PAC; and do projective Hilbertian fields have pro-free absolute Galois group (includes Shafarevich's conjecture)?
Author: Karl H. Hofmann
Publisher: Walter de Gruyter GmbH & Co KG
ISBN: 3110696010
Category : Mathematics
Languages : en
Pages : 1398
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Book Description
This book is designed both as a textbook for high-level graduate courses and as a reference for researchers who need to apply the structure and representation theory of compact groups. A gentle introduction to compact groups and their representation theory is followed by self-contained courses on linear and compact Lie groups, and on locally compact abelian groups. This fourth edition was updated with the latest developments in the field.
Author: Jakob Stix
Publisher: Springer
ISBN: 3642306748
Category : Mathematics
Languages : en
Pages : 257
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Book Description
The section conjecture in anabelian geometry, announced by Grothendieck in 1983, is concerned with a description of the set of rational points of a hyperbolic algebraic curve over a number field in terms of the arithmetic of its fundamental group. While the conjecture is still open today in 2012, its study has revealed interesting arithmetic for curves and opened connections, for example, to the question whether the Brauer-Manin obstruction is the only one against rational points on curves. This monograph begins by laying the foundations for the space of sections of the fundamental group extension of an algebraic variety. Then, arithmetic assumptions on the base field are imposed and the local-to-global approach is studied in detail. The monograph concludes by discussing analogues of the section conjecture created by varying the base field or the type of variety, or by using a characteristic quotient or its birational analogue in lieu of the fundamental group extension.
Author: Stéphane Ballet
Publisher: American Mathematical Soc.
ISBN: 1470454262
Category : Education
Languages : en
Pages : 303
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Book Description
This volume contains the proceedings of the 17th International Conference on Arithmetic, Geometry, Cryptography and Coding Theory (AGC2T-17), held from June 10–14, 2019, at the Centre International de Rencontres Mathématiques in Marseille, France. The conference was dedicated to the memory of Gilles Lachaud, one of the founding fathers of the AGC2T series. Since the first meeting in 1987 the biennial AGC2T meetings have brought together the leading experts on arithmetic and algebraic geometry, and the connections to coding theory, cryptography, and algorithmic complexity. This volume highlights important new developments in the field.
Author: Yuri Tschinkel
Publisher: Springer Science & Business Media
ISBN: 0817647473
Category : Mathematics
Languages : en
Pages : 700
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Book Description
EMAlgebra, Arithmetic, and Geometry: In Honor of Yu. I. ManinEM consists of invited expository and research articles on new developments arising from Manin’s outstanding contributions to mathematics.
Author: 中村博昭
Publisher: Advanced Studies in Pure Mathe
ISBN: 9784864970143
Category : Mathematics
Languages : en
Pages : 0
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Book Description
From the 1980's, Grothendieck's "Esquisse d'un Programme" triggered tremendous developments in number theory and arithmetic geometry, extending from the studies of anabelian geometry and related Galois representations to those of polylogarithms and multiple zeta values, motives, rational points on arithmetic varieties, and effectiveness questions in arithmetic geometry. The present volume collects twenty-four articles written by speakers (and their coauthors) of two international meetings focused on the above themes held in Kyoto in October 2010. It includes both survey articles and research papers which provide useful information about this area of investigation.Published by Mathematical Society of Japan and distributed by World Scientific Publishing Co. for all markets except North America
Author: Helmut Völklein
Publisher: Cambridge University Press
ISBN: 9780521562805
Category : Mathematics
Languages : en
Pages : 270
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Book Description
Develops the mathematical background and recent results on the Inverse Galois Problem.
