Lectures on Arakelov Geometry PDF Download
Are you looking for read ebook online? Search for your book and save it on your Kindle device, PC, phones or tablets. Download Lectures on Arakelov Geometry PDF full book. Access full book title Lectures on Arakelov Geometry by C. Soulé. Download full books in PDF and EPUB format.
Author: C. Soulé
Publisher: Cambridge University Press
ISBN: 9780521477093
Category : Mathematics
Languages : en
Pages : 190
Get Book Here
Book Description
An account for graduate students of this new technique in diophantine geometry; includes account of higher dimensional theory.
Author: C. Soulé
Publisher: Cambridge University Press
ISBN: 9780521477093
Category : Mathematics
Languages : en
Pages : 190
Get Book Here
Book Description
An account for graduate students of this new technique in diophantine geometry; includes account of higher dimensional theory.
Author: Gerd Faltings
Publisher: Princeton University Press
ISBN: 1400882478
Category : Mathematics
Languages : en
Pages : 113
Get Book Here
Book Description
The arithmetic Riemann-Roch Theorem has been shown recently by Bismut-Gillet-Soul. The proof mixes algebra, arithmetic, and analysis. The purpose of this book is to give a concise introduction to the necessary techniques, and to present a simplified and extended version of the proof. It should enable mathematicians with a background in arithmetic algebraic geometry to understand some basic techniques in the rapidly evolving field of Arakelov-theory.
Author: Emmanuel Peyre
Publisher: Springer Nature
ISBN: 3030575594
Category : Mathematics
Languages : en
Pages : 473
Get Book Here
Book Description
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.
Author: G. Cornell
Publisher: Springer Science & Business Media
ISBN: 1461386551
Category : Mathematics
Languages : en
Pages : 359
Get Book Here
Book Description
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.
Author: Robert J. Zimmer
Publisher: University of Chicago Press
ISBN: 0226237893
Category : Mathematics
Languages : en
Pages : 659
Get Book Here
Book Description
The study of group actions is more than 100 years old but remains a widely studied topic in a variety of mathematic fields. A central development in the last 50 years is the phenomenon of rigidity, whereby one can classify actions of certain groups. This book looks at rigidity.
Author: Arthur Ogus
Publisher: Cambridge University Press
ISBN: 1107187737
Category : Mathematics
Languages : en
Pages : 559
Get Book Here
Book Description
A self-contained introduction to logarithmic geometry, a key tool for analyzing compactification and degeneration in algebraic geometry.
Author: Huayi Chen
Publisher: Springer
ISBN: 9789811517273
Category : Mathematics
Languages : en
Pages : 452
Get Book Here
Book Description
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.
Author: Vasudevan Srinivas
Publisher: Springer Science & Business Media
ISBN: 1489967354
Category : Science
Languages : en
Pages : 328
Get Book Here
Book Description
Author: Kazuhiro Konno
Publisher: World Scientific
ISBN: 9814486736
Category : Mathematics
Languages : en
Pages : 273
Get Book Here
Book Description
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.
Author: Enrico Bombieri
Publisher: Cambridge University Press
ISBN: 9780521712293
Category : Mathematics
Languages : en
Pages : 676
Get Book Here
Book Description
This monograph is a bridge between the classical theory and modern approach via arithmetic geometry.
