Positivity In Arakelov Geometry Over Adelic Curves
DOWNLOAD
Download Positivity In Arakelov Geometry Over Adelic Curves PDF/ePub or read online books in Mobi eBooks. Click Download or Read Online button to get Positivity In Arakelov Geometry Over Adelic Curves book now. This website allows unlimited access to, at the time of writing, more than 1.5 million titles, including hundreds of thousands of titles in various foreign languages. If the content not found or just blank you must refresh this page
Positivity In Arakelov Geometry Over Adelic Curves
DOWNLOAD
Author : Huayi Chen
language : en
Publisher: Springer Nature
Release Date : 2024-08-21
Positivity In Arakelov Geometry Over Adelic Curves written by Huayi Chen and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-08-21 with Mathematics categories.
This monograph presents new research on Arakelov geometry over adelic curves, a novel theory of arithmetic geometry developed by the authors. It explores positivity conditions and establishes the Hilbert-Samuel formula and the equidistribution theorem in the context of adelic curves. Connections with several classical topics in Arakelov geometry and Diophantine geometry are highlighted, such as the arithmetic Hilbert-Samuel formula, positivity of line bundles, equidistribution of small subvarieties, and theorems resembling the Bogomolov conjecture. Detailed proofs and explanations are provided to ensure the text is accessible to both graduate students and experienced researchers.
Arakelov Geometry Over Adelic Curves
DOWNLOAD
Author : Huayi Chen
language : en
Publisher: Springer Nature
Release Date : 2020-01-29
Arakelov Geometry Over Adelic Curves written by Huayi Chen and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-01-29 with Mathematics categories.
The purpose of this book is to build the fundament of an Arakelov theory over adelic curves in order to provide a unified framework for research on arithmetic geometry in several directions. By adelic curve is meant a field equipped with a family of absolute values parametrized by a measure space, such that the logarithmic absolute value of each non-zero element of the field is an integrable function on the measure space. In the literature, such construction has been discussed in various settings which are apparently transversal to each other. The authors first formalize the notion of adelic curves and discuss in a systematic way its algebraic covers, which are important in the study of height theory of algebraic points beyond Weil–Lang’s height theory. They then establish a theory of adelic vector bundles on adelic curves, which considerably generalizes the classic geometry of vector bundles or that of Hermitian vector bundles over an arithmetic curve. They focus on an analogue of the slope theory in the setting of adelic curves and in particular estimate the minimal slope of tensor product adelic vector bundles. Finally, by using the adelic vector bundles as a tool, a birational Arakelov geometry for projective variety over an adelic curve is developed. As an application, a vast generalization of Nakai–Moishezon’s criterion of positivity is proven in clarifying the arguments of geometric nature from several fundamental results in the classic geometry of numbers. Assuming basic knowledge of algebraic geometry and algebraic number theory, the book is almost self-contained. It is suitable for researchers in arithmetic geometry as well as graduate students focusing on these topics for their doctoral theses.
Arakelov Geometry And Diophantine Applications
DOWNLOAD
Author : Emmanuel Peyre
language : en
Publisher: Springer Nature
Release Date : 2021-03-10
Arakelov Geometry And Diophantine Applications written by Emmanuel Peyre and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-03-10 with Mathematics categories.
Bridging the gap between novice and expert, the aim of this book is to present in a self-contained way a number of striking examples of current diophantine problems to which Arakelov geometry has been or may be applied. Arakelov geometry can be seen as a link between algebraic geometry and diophantine geometry. Based on lectures from a summer school for graduate students, this volume consists of 12 different chapters, each written by a different author. The first chapters provide some background and introduction to the subject. These are followed by a presentation of different applications to arithmetic geometry. The final part describes the recent application of Arakelov geometry to Shimura varieties and the proof of an averaged version of Colmez's conjecture. This book thus blends initiation to fundamental tools of Arakelov geometry with original material corresponding to current research. This book will be particularly useful for graduate students and researchers interested in the connections between algebraic geometry and number theory. The prerequisites are some knowledge of number theory and algebraic geometry.
Motivic Integration And Its Interactions With Model Theory And Non Archimedean Geometry Volume 2
DOWNLOAD
Author : Raf Cluckers
language : en
Publisher: Cambridge University Press
Release Date : 2011-09-22
Motivic Integration And Its Interactions With Model Theory And Non Archimedean Geometry Volume 2 written by Raf Cluckers 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 2011-09-22 with Mathematics categories.
The development of Maxim Kontsevich's initial ideas on motivic integration has unexpectedly influenced many other areas of mathematics, ranging from the Langlands program over harmonic analysis, to non-Archimedean analysis, singularity theory and birational geometry. This book assembles the different theories of motivic integration and their applications for the first time, allowing readers to compare different approaches and assess their individual strengths. All of the necessary background is provided to make the book accessible to graduate students and researchers from algebraic geometry, model theory and number theory. Applications in several areas are included so that readers can see motivic integration at work in other domains. In a rapidly-evolving area of research this book will prove invaluable. This second volume discusses various applications of non-Archimedean geometry, model theory and motivic integration and the interactions between these domains.
Algebra Arithmetic And Geometry
DOWNLOAD
Author : Yuri Tschinkel
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-08-05
Algebra Arithmetic And Geometry written by Yuri Tschinkel 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 2010-08-05 with Mathematics categories.
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.
Tropical And Non Archimedean Geometry
DOWNLOAD
Author : Omid Amini
language : en
Publisher: American Mathematical Soc.
Release Date : 2014-12-26
Tropical And Non Archimedean Geometry written by Omid Amini 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 2014-12-26 with Mathematics categories.
Over the past decade, it has become apparent that tropical geometry and non-Archimedean geometry should be studied in tandem; each subject has a great deal to say about the other. This volume is a collection of articles dedicated to one or both of these disciplines. Some of the articles are based, at least in part, on the authors' lectures at the 2011 Bellairs Workshop in Number Theory, held from May 6-13, 2011, at the Bellairs Research Institute, Holetown, Barbados. Lecture topics covered in this volume include polyhedral structures on tropical varieties, the structure theory of non-Archimedean curves (algebraic, analytic, tropical, and formal), uniformisation theory for non-Archimedean curves and abelian varieties, and applications to Diophantine geometry. Additional articles selected for inclusion in this volume represent other facets of current research and illuminate connections between tropical geometry, non-Archimedean geometry, toric geometry, algebraic graph theory, and algorithmic aspects of systems of polynomial equations.
Proceedings Of The Symposium On Algebraic Geometry In East Asia
DOWNLOAD
Author : Akira Ohbuchi
language : en
Publisher: World Scientific
Release Date : 2002
Proceedings Of The Symposium On Algebraic Geometry In East Asia written by Akira Ohbuchi and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002 with Mathematics categories.
This book is the proceedings of the conference ?Algebraic Geometry in East Asia? which was held in International Institute for Advanced Studies (IIAS) during August 3 to August 10, 2001.As the breadth of the topics covered in this proceedings demonstrate, the conference was indeed successful in assembling a wide spectrum of East Asian mathematicians, and gave them a welcome chance to discuss current state of algebraic geometry.
Algebraic Geometry In East Asia Proceedings Of The Symposium
DOWNLOAD
Author : Kazuhiro Konno
language : en
Publisher: World Scientific
Release Date : 2003-01-17
Algebraic Geometry In East Asia Proceedings Of The Symposium written by Kazuhiro Konno and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-01-17 with Mathematics categories.
This book is the proceedings of the conference “Algebraic Geometry in East Asia” which was held in International Institute for Advanced Studies (IIAS) during August 3 to August 10, 2001.As the breadth of the topics covered in this proceedings demonstrate, the conference was indeed successful in assembling a wide spectrum of East Asian mathematicians, and gave them a welcome chance to discuss current state of algebraic geometry.
The Arithmetic Of Polynomial Dynamical Pairs
DOWNLOAD
Author : Charles Favre
language : en
Publisher: Princeton University Press
Release Date : 2022-06-14
The Arithmetic Of Polynomial Dynamical Pairs written by Charles Favre 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 2022-06-14 with Mathematics categories.
New mathematical research in arithmetic dynamics In The Arithmetic of Polynomial Dynamical Pairs, Charles Favre and Thomas Gauthier present new mathematical research in the field of arithmetic dynamics. Specifically, the authors study one-dimensional algebraic families of pairs given by a polynomial with a marked point. Combining tools from arithmetic geometry and holomorphic dynamics, they prove an “unlikely intersection” statement for such pairs, thereby demonstrating strong rigidity features for them. They further describe one-dimensional families in the moduli space of polynomials containing infinitely many postcritically finite parameters, proving the dynamical André-Oort conjecture for curves in this context, originally stated by Baker and DeMarco. This is a reader-friendly invitation to a new and exciting research area that brings together sophisticated tools from many branches of mathematics.
Geometric Methods In Algebra And Number Theory
DOWNLOAD
Author : Fedor Bogomolov
language : en
Publisher: Springer Science & Business Media
Release Date : 2004-11-12
Geometric Methods In Algebra And Number Theory written by Fedor Bogomolov 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 2004-11-12 with Mathematics categories.
* Contains a selection of articles exploring geometric approaches to problems in algebra, algebraic geometry and number theory * The collection gives a representative sample of problems and most recent results in algebraic and arithmetic geometry * Text can serve as an intense introduction for graduate students and those wishing to pursue research in algebraic and arithmetic geometry