Author: Gerd Faltings
Publisher: Princeton University Press
ISBN: 0691025444
Category : Mathematics
Languages : en
Pages : 112
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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: Gerd Faltings
Publisher:
ISBN: 9780691087719
Category : Geometry, Algebraic
Languages : en
Pages : 100
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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: Gerd Faltings
Publisher: Princeton University Press
ISBN: 1400882478
Category : Mathematics
Languages : en
Pages : 118
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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: Shai M. J. Haran
Publisher: American Mathematical Soc.
ISBN: 147042312X
Category : Arithmetical algebraic geometry
Languages : en
Pages : 202
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Book Description
To view the abstract go to http://www.ams.org/books/memo/1166.
Author: Emmanuel Peyre
Publisher: Springer Nature
ISBN: 3030575594
Category : Mathematics
Languages : en
Pages : 469
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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: Sylvain Cappell
Publisher: Princeton University Press
ISBN: 9780691088143
Category :
Languages : en
Pages : 452
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Author: Seminario matematico (Turin, Italy)
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 536
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Author: Patrick Popescu-Pampu
Publisher: Springer
ISBN: 3319423126
Category : Mathematics
Languages : en
Pages : 184
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Book Description
Exploring several of the evolutionary branches of the mathematical notion of genus, this book traces the idea from its prehistory in problems of integration, through algebraic curves and their associated Riemann surfaces, into algebraic surfaces, and finally into higher dimensions. Its importance in analysis, algebraic geometry, number theory and topology is emphasized through many theorems. Almost every chapter is organized around excerpts from a research paper in which a new perspective was brought on the genus or on one of the objects to which this notion applies. The author was motivated by the belief that a subject may best be understood and communicated by studying its broad lines of development, feeling the way one arrives at the definitions of its fundamental notions, and appreciating the amount of effort spent in order to explore its phenomena.
Author:
Publisher:
ISBN:
Category : American literature
Languages : en
Pages : 3126
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Book Description
Author:
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 680
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Book Description
