Arakelov Geometry is popular PDF and ePub book, written by Atsushi Moriwaki in 2014-11-05, it is a fantastic choice for those who relish reading online the Mathematics genre. Let's immerse ourselves in this engaging Mathematics book by exploring the summary and details provided below. Remember, Arakelov Geometry can be Read Online from any device for your convenience.
Arakelov Geometry Book PDF Summary
The main goal of this book is to present the so-called birational Arakelov geometry, which can be viewed as an arithmetic analog of the classical birational geometry, i.e., the study of big linear series on algebraic varieties. After explaining classical results about the geometry of numbers, the author starts with Arakelov geometry for arithmetic curves, and continues with Arakelov geometry of arithmetic surfaces and higher-dimensional varieties. The book includes such fundamental results as arithmetic Hilbert-Samuel formula, arithmetic Nakai-Moishezon criterion, arithmetic Bogomolov inequality, the existence of small sections, the continuity of arithmetic volume function, the Lang-Bogomolov conjecture and so on. In addition, the author presents, with full details, the proof of Faltings' Riemann-Roch theorem. Prerequisites for reading this book are the basic results of algebraic geometry and the language of schemes.
Detail Book of Arakelov Geometry PDF
- Author : Atsushi Moriwaki
- Release : 05 November 2014
- Publisher : American Mathematical Soc.
- ISBN : 9781470410742
- Genre : Mathematics
- Total Page : 298 pages
- Language : English
- PDF File Size : 11,9 Mb
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