Introductory notes on valuation rings and function fields in one variable:
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| Main Authors: | , |
|---|---|
| Format: | Electronic eBook |
| Language: | English |
| Published: |
Pisa
Ed. della Normale
2014
|
| Series: | Appunti
14 |
| Online Access: | Inhaltsverzeichnis |
| ISBN: | 9788876425004 |
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MARC
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|---|---|
| adam_text | Contents
Preface
vii
Introduction
Generalities on algebraic functions of one
variabile
1
1
A first viewpoint for algebraic functions: Riemarm surfaces
3
2
A second viewpoint: geometry of curves
......... 4
3
A third viewpoint: fields
................. 5
1
Basic notions on function fields of one variable
7
1.1
Function fields of one variable, rational fields
...... 7
1.1.1
Unirational and rational function fields
..... 11
1.2
Function fields (of one variable) define (plane) curves
. . 16
1.3
Algebraic varieties, rings of regular functions
...... 23
1.4
Field inclusions and rational maps
............ 25
2
Valuation rings
31
2.1
Valuation rings and places
................. 31
2.1.1
Some significant examples
............ 34
2.2
Existence and extensions of valuation rings
....... 36
2.2.1
Some applications of Theorem
2.2.1....... 38
2.3
Discrete valuation rings
.................. 42
2.4
Simultaneous approximations with several discrete valu¬
ation rings
......................... 49
2.5
Extension of discrete valuation rings
........... 50
2.6
Completions of discrete valuation rings
......... 61
2.6.1
On valuation rings and geometric points
agam
. . 70
2.7
Notes to Chapter
2 .................... 83
A Hubert s NuUstellensatz
85
АЛ
Generalities
.....-.................. 85
АЛЛ
Preliminaries on algebraic sets
........... 86
vi
Renata
Scognamillo
and Umberto
Zarmier
A
.2
Proof of the double implication weak form
О
strong
form
........................... 88
В
Puiseixx series
95
В
.1
Field of definition, convergence and
Eisenstein
Theorem
95
С
Discrete valuation rings and Dedekind domains
107
C.I Dedekind domains
.................... 107
C.2 Factorization
....................... 109
C.3 Notes to appendices
.....................
Ill
References
113
Index
115
|
| any_adam_object | 1 |
| author | Scognamillo, Renata Zannier, Umberto 1957- |
| author_GND | (DE-588)102371471X |
| author_facet | Scognamillo, Renata Zannier, Umberto 1957- |
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| bvnumber | BV042083878 |
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| indexdate | 2024-07-10T01:12:17Z |
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| isbn | 9788876425004 |
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| spelling | Scognamillo, Renata Verfasser aut Introductory notes on valuation rings and function fields in one variable Renata Scognamillo and Umberto Zannier Pisa Ed. della Normale 2014 txt rdacontent c rdamedia cr rdacarrier Appunti 14 Zannier, Umberto 1957- Verfasser (DE-588)102371471X aut Appunti 14 (DE-604)BV021797181 14 Digitalisierung UB Regensburg - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027524898&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Scognamillo, Renata Zannier, Umberto 1957- Introductory notes on valuation rings and function fields in one variable Appunti |
| title | Introductory notes on valuation rings and function fields in one variable |
| title_auth | Introductory notes on valuation rings and function fields in one variable |
| title_exact_search | Introductory notes on valuation rings and function fields in one variable |
| title_full | Introductory notes on valuation rings and function fields in one variable Renata Scognamillo and Umberto Zannier |
| title_fullStr | Introductory notes on valuation rings and function fields in one variable Renata Scognamillo and Umberto Zannier |
| title_full_unstemmed | Introductory notes on valuation rings and function fields in one variable Renata Scognamillo and Umberto Zannier |
| title_short | Introductory notes on valuation rings and function fields in one variable |
| title_sort | introductory notes on valuation rings and function fields in one variable |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027524898&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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