Download or read book Galois Teichm ller Theory and Arithmetic Geometry written by Hiroaki Nakamura and published by . This book was released on 2018 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Galois Covers Grothendieck Teichm ller Theory and Dessins d Enfants written by Frank Neumann and published by Springer Nature. This book was released on 2020-09-26 with total page 240 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Galois Teichmu ller Theory and Arithmetic Geometry written by 中村博昭 and published by Advanced Studies in Pure Mathe. This book was released on 2012-10 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Download or read book Arithmetic Geometry written by Nancy Childress and published by American Mathematical Soc.. This book was released on 1994 with total page 234 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book resulted from a research conference in arithmetic geometry held at Arizona State University in March 1993. The papers describe important recent advances in arithmetic geometry. Several articles deal with p-adic modular forms of half-integral weight and their roles in arithmetic geometry. The volume also contains material on the Iwasawa theory of cyclotomic fields, elliptic curves, and function fields, including p-adic L-functions and p-adic height pairings. Other articles focus on the inverse Galois problem, fields of definition of abelian varieties with real multiplication, and computation of torsion groups of elliptic curves. The volume also contains a previously unpublished letter of John Tate, written to J.-P. Serre in 1973, concerning Serre's conjecture on Galois representations. With contributions by some of the leading experts in the field, this book provides a look at the state of the art in arithmetic geometry.
Download or read book Foundations of p adic Teichmuller Theory written by Shinichi Mochizuki and published by American Mathematical Soc.. This book was released on 2014-01-06 with total page 546 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book An Invitation to Arithmetic Geometry written by Dino Lorenzini and published by American Mathematical Soc.. This book was released on 1996-02-22 with total page 418 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.
Download or read book Handbook of Teichm ller Theory written by Athanase Papadopoulos and published by European Mathematical Society. This book was released on 2007 with total page 812 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Teichmuller space of a surface was introduced by O. Teichmuller in the 1930s. It is a basic tool in the study of Riemann's moduli spaces and the mapping class groups. These objects are fundamental in several fields of mathematics, including algebraic geometry, number theory, topology, geometry, and dynamics. The original setting of Teichmuller theory is complex analysis. The work of Thurston in the 1970s brought techniques of hyperbolic geometry to the study of Teichmuller space and its asymptotic geometry. Teichmuller spaces are also studied from the point of view of the representation theory of the fundamental group of the surface in a Lie group $G$, most notably $G=\mathrm{PSL}(2,\mathbb{R})$ and $G=\mathrm{PSL}(2,\mathbb{C})$. In the 1980s, there evolved an essentially combinatorial treatment of the Teichmuller and moduli spaces involving techniques and ideas from high-energy physics, namely from string theory. The current research interests include the quantization of Teichmuller space, the Weil-Petersson symplectic and Poisson geometry of this space as well as gauge-theoretic extensions of these structures. The quantization theories can lead to new invariants of hyperbolic 3-manifolds. The purpose of this handbook is to give a panorama of some of the most important aspects of Teichmuller theory. The handbook should be useful to specialists in the field, to graduate students, and more generally to mathematicians who want to learn about the subject. All the chapters are self-contained and have a pedagogical character. They are written by leading experts in the subject.
Download or read book Progress in Galois Theory written by Helmut Voelklein and published by Springer Science & Business Media. This book was released on 2006-08-10 with total page 174 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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).
Download or read book Teichm ller Theory in Riemannian Geometry written by Anthony Tromba and published by Birkhäuser. This book was released on 2012-12-06 with total page 224 pages. Available in PDF, EPUB and Kindle. Book excerpt: These lecture notes are based on the joint work of the author and Arthur Fischer on Teichmiiller theory undertaken in the years 1980-1986. Since then many of our colleagues have encouraged us to publish our approach to the subject in a concise format, easily accessible to a broad mathematical audience. However, it was the invitation by the faculty of the ETH Ziirich to deliver the ETH N achdiplom-Vorlesungen on this material which provided the opportunity for the author to develop our research papers into a format suitable for mathematicians with a modest background in differential geometry. We also hoped it would provide the basis for a graduate course stressing the application of fundamental ideas in geometry. For this opportunity the author wishes to thank Eduard Zehnder and Jiirgen Moser, acting director and director of the Forschungsinstitut fiir Mathematik at the ETH, Gisbert Wiistholz, responsible for the Nachdiplom Vorlesungen and the entire ETH faculty for their support and warm hospitality. This new approach to Teichmiiller theory presented here was undertaken for two reasons. First, it was clear that the classical approach, using the theory of extremal quasi-conformal mappings (in this approach we completely avoid the use of quasi-conformal maps) was not easily applicable to the theory of minimal surfaces, a field of interest of the author over many years. Second, many other active mathematicians, who at various times needed some Teichmiiller theory, have found the classical approach inaccessible to them.
Download or read book Arithmetic Geometry written by G. Cornell and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 359 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is the result of a (mainly) instructional conference on arithmetic geometry, held from July 30 through August 10, 1984 at the University of Connecticut in Storrs. This volume contains expanded versions of almost all the instructional lectures given during the conference. In addition to these expository lectures, this volume contains a translation into English of Falt ings' seminal paper which provided the inspiration for the conference. We thank Professor Faltings for his permission to publish the translation and Edward Shipz who did the translation. We thank all the people who spoke at the Storrs conference, both for helping to make it a successful meeting and enabling us to publish this volume. We would especially like to thank David Rohrlich, who delivered the lectures on height functions (Chapter VI) when the second editor was unavoidably detained. In addition to the editors, Michael Artin and John Tate served on the organizing committee for the conference and much of the success of the conference was due to them-our thanks go to them for their assistance. Finally, the conference was only made possible through generous grants from the Vaughn Foundation and the National Science Foundation.
Download or read book Geometric Galois Actions Volume 2 The Inverse Galois Problem Moduli Spaces and Mapping Class Groups written by Leila Schneps and published by Cambridge University Press. This book was released on 1997-08-07 with total page 363 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Moduli Spaces of Riemann Surfaces written by Benson Farb and published by American Mathematical Soc.. This book was released on 2013-08-16 with total page 371 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mapping class groups and moduli spaces of Riemann surfaces were the topics of the Graduate Summer School at the 2011 IAS/Park City Mathematics Institute. This book presents the nine different lecture series comprising the summer school, covering a selection of topics of current interest. The introductory courses treat mapping class groups and Teichmüller theory. The more advanced courses cover intersection theory on moduli spaces, the dynamics of polygonal billiards and moduli spaces, the stable cohomology of mapping class groups, the structure of Torelli groups, and arithmetic mapping class groups. The courses consist of a set of intensive short lectures offered by leaders in the field, designed to introduce students to exciting, current research in mathematics. These lectures do not duplicate standard courses available elsewhere. The book should be a valuable resource for graduate students and researchers interested in the topology, geometry and dynamics of moduli spaces of Riemann surfaces and related topics. Titles in this series are co-published with the Institute for Advanced Study/Park City Mathematics Institute. Members of the Mathematical Association of America (MAA) and the National Council of Teachers of Mathematics (NCTM) receive a 20% discount from list price.
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:
Download or read book Periods in Quantum Field Theory and Arithmetic written by José Ignacio Burgos Gil and published by Springer Nature. This book was released on 2020-03-14 with total page 631 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is the outcome of research initiatives formed during the special ``Research Trimester on Multiple Zeta Values, Multiple Polylogarithms, and Quantum Field Theory'' at the ICMAT (Instituto de Ciencias Matemáticas, Madrid) in 2014. The activity was aimed at understanding and deepening recent developments where Feynman and string amplitudes on the one hand, and periods and multiple zeta values on the other, have been at the heart of lively and fruitful interactions between theoretical physics and number theory over the past few decades. In this book, the reader will find research papers as well as survey articles, including open problems, on the interface between number theory, quantum field theory and string theory, written by leading experts in the respective fields. Topics include, among others, elliptic periods viewed from both a mathematical and a physical standpoint; further relations between periods and high energy physics, including cluster algebras and renormalisation theory; multiple Eisenstein series and q-analogues of multiple zeta values (also in connection with renormalisation); double shuffle and duality relations; alternative presentations of multiple zeta values using Ecalle's theory of moulds and arborification; a distribution formula for generalised complex and l-adic polylogarithms; Galois action on knots. Given its scope, the book offers a valuable resource for researchers and graduate students interested in topics related to both quantum field theory, in particular, scattering amplitudes, and number theory.
Download or read book Handbook of Teichm ller Theory written by Athanase Papadopoulos and published by . This book was released on with total page 874 pages. Available in PDF, EPUB and Kindle. Book excerpt: The subject of this handbook is Teichmüller theory in a wide sense, namely the theory of geometric structures on surfaces and their moduli spaces. This includes the study of vector bundles on these moduli spaces, the study of mapping class groups, the relation with 3-manifolds, the relation with symmetric spaces and arithmetic groups, the representation theory of fundamental groups, and applications to physics. Thus the handbook is a place where several fields of mathematics interact: Riemann surfaces, hyperbolic geometry, partial differential equations, several complex variables, algebraic geometry, algebraic topology, combinatorial topology, low-dimensional topology, theoretical physics, and others. This confluence of ideas towards a unique subject is a manifestation of the unity and harmony of mathematics. The present volume contains surveys on the fundamental theory as well as surveys on applications to and relations with the fields mentioned above. It is written by leading experts in the fields. Some of the surveys contain classical material, while others present the latest developments of the theory as well as open problems. The metric and the analytic theory. The group theory. The algebraic topology of mapping class groups and moduli spaces. Teichmüller theory and mathematical physics. The handbook is addressed to graduate students and researchers in all the fields mentioned.
Download or read book Lectures on the Theory of Pure Motives written by Jacob P. Murre and published by American Mathematical Soc.. This book was released on 2013-04-11 with total page 163 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory of motives was created by Grothendieck in the 1960s as he searched for a universal cohomology theory for algebraic varieties. The theory of pure motives is well established as far as the construction is concerned. Pure motives are expected to h
Download or read book Automorphic Forms and Galois Representations written by Fred Diamond and published by Cambridge University Press. This book was released on 2014-10-16 with total page 387 pages. Available in PDF, EPUB and Kindle. Book excerpt: Part two of a two-volume collection exploring recent developments in number theory related to automorphic forms and Galois representations.
