Galois-Teichmüller Theory and Arithmetic Geometry PDF Download

Author: Hiroaki Nakamura
Publisher:
ISBN: 9784864970136
Category :
Languages : en
Pages :

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Author: 中村博昭
Publisher: Advanced Studies in Pure Mathe
ISBN: 9784864970143
Category : Mathematics
Languages : en
Pages : 0

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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: Frank Neumann
Publisher: Springer Nature
ISBN: 3030517950
Category : Mathematics
Languages : en
Pages : 240

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This book presents original peer-reviewed contributions from the London Mathematical Society (LMS) Midlands Regional Meeting and Workshop on 'Galois Covers, Grothendieck-Teichmüller Theory and Dessinsd'Enfants', which took place at the University of Leicester, UK, from 4 to 7 June, 2018. Within the theme of the workshop, the collected articles cover a broad range of topics and explore exciting new links between algebraic geometry, representation theory, group theory, number theory and algebraic topology. The book combines research and overview articles by prominent international researchers and provides a valuable resource for researchers and students alike.

Author: Helmut Voelklein
Publisher: Springer Science & Business Media
ISBN: 0387235345
Category : Mathematics
Languages : en
Pages : 174

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The legacy of Galois was the beginning of Galois theory as well as group theory. From this common origin, the development of group theory took its own course, which led to great advances in the latter half of the 20th cen tury. It was John Thompson who shaped finite group theory like no-one else, leading the way towards a major milestone of 20th century mathematics, the classification of finite simple groups. After the classification was announced around 1980, it was again J. Thomp son who led the way in exploring its implications for Galois theory. The first question is whether all simple groups occur as Galois groups over the rationals (and related fields), and secondly, how can this be used to show that all finite groups occur (the 'Inverse Problem of Galois Theory'). What are the implica tions for the stmcture and representations of the absolute Galois group of the rationals (and other fields)? Various other applications to algebra and number theory have been found, most prominently, to the theory of algebraic curves (e.g., the Guralnick-Thompson Conjecture on the Galois theory of covers of the Riemann sphere).

Author: Lin Weng
Publisher: World Scientific
ISBN: 981256814X
Category : Mathematics
Languages : en
Pages : 411

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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: Shinichi Mochizuki
Publisher: American Mathematical Soc.
ISBN: 1470412268
Category : Mathematics
Languages : en
Pages : 546

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This book lays the foundation for a theory of uniformization of p-adic hyperbolic curves and their moduli. On one hand, this theory generalizes the Fuchsian and Bers uniformizations of complex hyperbolic curves and their moduli to nonarchimedian places. That is why in this book, the theory is referred to as p-adic Teichmüller theory, for short. On the other hand, the theory may be regarded as a fairly precise hyperbolic analog of the Serre-Tate theory of ordinary abelian varieties and their moduli. The theory of uniformization of p-adic hyperbolic curves and their moduli was initiated in a previous work by Mochizuki. And in some sense, this book is a continuation and generalization of that work. This book aims to bridge the gap between the approach presented and the classical uniformization of a hyperbolic Riemann surface that is studied in undergraduate complex analysis. Features: Presents a systematic treatment of the moduli space of curves from the point of view of p-adic Galois representations.Treats the analog of Serre-Tate theory for hyperbolic curves.Develops a p-adic analog of Fuchsian and Bers uniformization theories.Gives a systematic treatment of a "nonabelian example" of p-adic Hodge theory. Titles in this series are co-published with International Press of Boston, Inc., Cambridge, MA.

Author: Leila Schneps
Publisher: Cambridge University Press
ISBN: 0521596416
Category : Mathematics
Languages : en
Pages : 363

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This book surveys progress in the domains described in the hitherto unpublished manuscript "Esquisse d'un Programme" (Sketch of a Program) by Alexander Grothendieck. It will be of wide interest amongst workers in algebraic geometry, number theory, algebra and topology.

Author: Pierre Dèbes
Publisher: Springer Science & Business Media
ISBN: 3034804873
Category : Mathematics
Languages : en
Pages : 411

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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: Leila Schneps
Publisher: Cambridge University Press
ISBN: 9780521596428
Category : Mathematics
Languages : en
Pages : 308

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The first of two companion volumes on anabelian algebraic geometry, this book contains the famous, but hitherto unpublished manuscript 'Esquisse d'un Programme' (Sketch of a Program) by Alexander Grothendieck. This work, written in 1984, fourteen years after his retirement from public life in mathematics, together with the closely connected letter to Gerd Faltings, dating from 1983 and also published for the first time in this volume, describe a powerful program of future mathematics, unifying aspects of geometry and arithmetic via the central point of moduli spaces of curves; it is written in an artistic and informal style. The book also contains several articles on subjects directly related to the ideas explored in the manuscripts; these are surveys of mathematics due to Grothendieck, explanations of points raised in the Esquisse, and surveys on progress in the domains described there.

Author: Helmut Völklein
Publisher: Cambridge University Press
ISBN: 9780521637473
Category : Mathematics
Languages : en
Pages : 294

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Collection of articles by leading experts in Galois theory, focusing on the Inverse Galois Problem.