图书信息
图书目录
函数域和数域赋值论导论（英文版）Elementary Valuation Theory in Function Fields and Number Fields
暂无简介
作者：
Umberto Zannier
定价：
89.00元
出版时间：
2025-12-12
ISBN：
978-7-04-064933-8
物料号：
64933-00
读者对象：
学术著作
一级分类：
自然科学
二级分类：
数学与统计
三级分类：
数论
重点项目：
暂无
版面字数：
240.00千字
开本：
16开
装帧形式：
平装
版次：
1
最新版次印刷时间：
2025-01-03
- 前辅文
- Chapter 1 Introduction: Generalities on algebraic functions of one variable
- 1.1 A first viewpoint for algebraic functions: Riemann surfaces
- 1.2 A second viewpoint: geometry of curves
- 1.3 A third viewpoint: fields
- Chapter 2 Basic notions on function fields of one variable
- 2.1 Function fields of one variable, rational fields
- 2.1.1 Unirational and rational function fields
- 2.2 Function fields (of one variable) define (plane) curves
- 2.3 Algebraic varieties, rings of regular functions
- 2.4 Field inclusions and rational maps
- 2.4.1 Birational equivalence
- 2.1 Function fields of one variable, rational fields
- Chapter 3 Valuation rings
- 3.1 Valuation rings and places
- 3.1.1 Some significant examples
- 3.2 Existence and extensions of valuation rings
- 3.2.1 Some applications of Theorem 3.1
- 3.3 Discrete valuation rings
- 3.4 Simultaneous approximations with several discrete valuation rings
- 3.5 Extensions of discrete valuation rings
- 3.6 Completions of discrete valuation rings
- 3.6.1 On valuation rings and geometric points again
- 3.6.2 Norms on vector spaces
- 3.7 Notes to Chapter 3
- 3.1 Valuation rings and places
- Appendix A Hilbert’s Nullstellensatz
- A.1 Generalities
- A.1.1 Review of preliminaries on algebraic sets
- A.2 Proofs
- A.2.1 Proof of the double implication ‘weak form’ ↔ ‘strong form’
- A.3 Two further applications
- A.1 Generalities
- Appendix B Puiseux series
- B.1 Field of definition, convergence, and Eisenstein theorem
- B.2 Algebraic functions and differential equations
- Appendix C Discrete valuation rings and Dedekind domains
- C.1 Dedekind domains
- C.2 Factorization
- C.3 Further notes to appendices
- Index
- References
