Topics Surrounding The Combinatorial Anabelian Geometry Of Hyperbolic Curves Ii

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Topics Surrounding The Combinatorial Anabelian Geometry Of Hyperbolic Curves Ii
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Author : Yuichiro Hoshi
language : en
Publisher: Springer Nature
Release Date : 2022-05-20
Topics Surrounding The Combinatorial Anabelian Geometry Of Hyperbolic Curves Ii written by Yuichiro Hoshi and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-05-20 with Mathematics categories.
The present monograph further develops the study, via the techniques of combinatorial anabelian geometry, of the profinite fundamental groups of configuration spaces associated to hyperbolic curves over algebraically closed fields of characteristic zero. The starting point of the theory of the present monograph is a combinatorial anabelian result which allows one to reduce issues concerning the anabelian geometry of configuration spaces to issues concerning the anabelian geometry of hyperbolic curves, as well as to give purely group-theoretic characterizations of the cuspidal inertia subgroups of one-dimensional subquotients of the profinite fundamental group of a configuration space. We then turn to the study of tripod synchronization, i.e., of the phenomenon that an outer automorphism of the profinite fundamental group of a log configuration space associated to a stable log curve induces the same outer automorphism on certain subquotients of such a fundamental group determined by tripods [i.e., copies of the projective line minus three points]. The theory of tripod synchronization shows that such outer automorphisms exhibit somewhat different behavior from the behavior that occurs in the case of discrete fundamental groups and, moreover, may be applied to obtain various strong results concerning profinite Dehn multi-twists. In the final portion of the monograph, we develop a theory of localizability, on the dual graph of a stable log curve, for the condition that an outer automorphism of the profinite fundamental group of the stable log curve lift to an outer automorphism of the profinite fundamental group of a corresponding log configuration space. This localizability is combined with the theory of tripod synchronization to construct a purely combinatorial analogue of the natural outer surjection from the étale fundamental group of the moduli stack of hyperbolic curves over the field of rational numbers to the absolute Galois group of the field of rational numbers.
Arithmetic And Geometry Around Galois Theory
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Author : Pierre Dèbes
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-13
Arithmetic And Geometry Around Galois Theory written by Pierre Dèbes 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 2012-12-13 with Mathematics categories.
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.
Current Developments In Algebraic Geometry
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Author : Lucia Caporaso
language : en
Publisher: Cambridge University Press
Release Date : 2012-03-19
Current Developments In Algebraic Geometry written by Lucia Caporaso 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 2012-03-19 with Mathematics categories.
This volume, based on a workshop by the MSRI, offers an overview of the state of the art in many areas of algebraic geometry.
Geometry And Quantization Of Moduli Spaces
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Author : Vladimir Fock
language : en
Publisher: Birkhäuser
Release Date : 2016-12-25
Geometry And Quantization Of Moduli Spaces written by Vladimir Fock and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-12-25 with Mathematics categories.
This volume is based on four advanced courses held at the Centre de Recerca Matemàtica (CRM), Barcelona. It presents both background information and recent developments on selected topics that are experiencing extraordinary growth within the broad research area of geometry and quantization of moduli spaces. The lectures focus on the geometry of moduli spaces which are mostly associated to compact Riemann surfaces, and are presented from both classical and quantum perspectives.
Topics Surrounding The Combinatorial Anabelian Geometry Of Hyperbolic Curves I
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Author : Yuichiro Hoshi
language : en
Publisher:
Release Date : 2011
Topics Surrounding The Combinatorial Anabelian Geometry Of Hyperbolic Curves I written by Yuichiro Hoshi and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011 with Curves, Algebraic categories.
Foundations Of P Adic Teichmuller Theory
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Author : Shinichi Mochizuki
language : en
Publisher: American Mathematical Soc.
Release Date : 2014-01-06
Foundations Of P Adic Teichmuller Theory written by Shinichi Mochizuki 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 2014-01-06 with Mathematics categories.
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.
Topics Surrounding The Combinatorial Anabelian Geometry Of Hyperbolic Curves Iii
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Author : Yuichiro Hoshi
language : en
Publisher:
Release Date : 2012
Topics Surrounding The Combinatorial Anabelian Geometry Of Hyperbolic Curves Iii written by Yuichiro Hoshi and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012 with Curves, Algebraic categories.
Mathematical Reviews
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Author :
language : en
Publisher:
Release Date : 2004
Mathematical Reviews written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004 with Mathematics categories.
Galois Teichmu Ller Theory And Arithmetic Geometry
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Author : 中村博昭
language : en
Publisher: Advanced Studies in Pure Mathe
Release Date : 2012-10
Galois Teichmu Ller Theory And Arithmetic Geometry written by 中村博昭 and has been published by Advanced Studies in Pure Mathe this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-10 with Mathematics categories.
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
The Mathematical And Philosophical Legacy Of Alexander Grothendieck
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Author : Marco Panza
language : en
Publisher: Springer Nature
Release Date : 2025-01-21
The Mathematical And Philosophical Legacy Of Alexander Grothendieck written by Marco Panza and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-01-21 with Mathematics categories.
Alexander Grothendieck is often considered one of the greatest mathematicians of the twentieth century (if not all time), and his unique vision continues to impact and inspire many fields and researchers today. Utilizing a multidisciplinary approach, this edited volume explores the profound influence his work and ideas have had not only on mathematics, but also on logic and philosophy. Chapters are written by international scholars, and many were inspired by talks given at the conference “Grothendieck, A Multifarious Giant” at Chapman University (May 24-28, 2022). Some chapters are written from a historical perspective and discuss the development of the main themes that characterized Grothendieck's work. Others are more mathematical in nature, analyzing and extending some of his more relevant and obscure results that are still not well understood. Philosophical implications and applications in logic are the subjects of other chapters. This volume will be of interest not only to mathematicians working in algebraic geometry, category theory, and other areas to which Grothendieck contributed, but also to philosophers, logicians, and historians of science.