Adelic divisors on arithmetic varieties:
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Providence, Rhode Island
American Mathematical Society
July 2016
|
| Series: | Memoirs of the American Mathematical Society
volume 242, number 1144 (1st of 4 numbers) |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | v, 122 Seiten |
| ISBN: | 9781470419264 |
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MARC
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Record in the Search Index
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| adam_text | Contents
Introduction 1
0.1. Birational Arakelov geometry 1
0.2. Green functions on analytic spaces over a compete discrete valuation
field 3
0.3. Adelic arithmetic divisors 3
0.4. Main results 5
0.5. Conventions and terminology 6
Chapter 1. Preliminaries 9
1.1. Lemmas 9
1.2. R-Cartier divisors on a noetherian integral scheme 15
1.3. Analytification of algebraic schemes over a complete valuation field 17
1.4. Green functions on complex varieties 19
Chapter 2. Adelic R-Cartier Divisors over a Discrete Valuation Field 23
2.1. Green functions on analytic spaces over a discrete valuation field 23
2.2. Definition of adelic R-Cartier divisors 28
2.3. Local degree 29
2.4. Local intersection number 29
Chapter 3. Local and Global Density Theorems 37
3.1. Vertical fractional ideal sheaves and birational system of models 37
3.2. Model functions 38
3.3. Density theorems 39
3.4. Zariski’s lemma for integrable functions 41
3.5. Radon measure arising from local intersection number 42
Chapter 4. Adelic Arithmetic R-Cartier Divisors 45
4.1. Definition and basic properties 45
4.2. Global degree 48
4.3. Volume of adelic arithmetic R-Cartier divisors 49
4.4. Positivity of adelic arithmetic R-Cartier divisors 50
4.5. Global intersection number 53
Chapter 5. Continuity of the Volume Function 61
5.1. Basic properties of the volume 61
5.2. Proof of the continuity of the volume function 67
5.3. Applications 70
Chapter 6. Zariski Decompositions of Adelic Arithmetic Divisors on
Arithmetic Surfaces 75
iii
IV
CONTENTS
6.1. Local Zariski decompositions of adelic divisors on algebraic curves 75
6.2. Proof of Zariski decompositions for adelic arithmetic divisors 81
Chapter 7. Characterization of Nef Adelic Arithmetic Divisors on Arithmetic
Surfaces 87
7.1. Hodge index theorem for adelic arithmetic divisors 87
7.2. Arithmetic asymptotic multiplicity 89
7.3. Necessary condition for the equality vol = volx 93
7.4. Numerical characterization 96
Chapter 8. Dirichlet’s unit Theorem for Adelic Arithmetic Divisors 99
8.1. Fundamental question for adelic divisors 99
8.2. Proof of Theorem 8.1.2 99
Appendix A. Characterization of Relatively Nef Cartier Divisors 107
A.l. Asymptotic multiplicity 107
A.2. Sectional decomposition 111
A.3. Characterization in terms of ¡j,w 112
Bibliography 117
Subject Index 119
Symbol Index 121
|
| any_adam_object | 1 |
| author | Moriwaki, Atsushi 1960- |
| author_GND | (DE-588)1068650419 |
| author_facet | Moriwaki, Atsushi 1960- |
| author_role | aut |
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| dewey-ones | 512 - Algebra |
| dewey-raw | 512.7/4 |
| dewey-search | 512.7/4 |
| dewey-sort | 3512.7 14 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
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| id | DE-604.BV043664292 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:31:54Z |
| institution | BVB |
| isbn | 9781470419264 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-029077582 |
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| physical | v, 122 Seiten |
| publishDate | 2016 |
| publishDateSearch | 2016 |
| publishDateSort | 2016 |
| publisher | American Mathematical Society |
| record_format | marc |
| series | Memoirs of the American Mathematical Society |
| series2 | Memoirs of the American Mathematical Society |
| spelling | Moriwaki, Atsushi 1960- (DE-588)1068650419 aut Adelic divisors on arithmetic varieties Atsushi Moriwaki Providence, Rhode Island American Mathematical Society July 2016 v, 122 Seiten txt rdacontent n rdamedia nc rdacarrier Memoirs of the American Mathematical Society volume 242, number 1144 (1st of 4 numbers) Memoirs of the American Mathematical Society volume 242, number 1144 (1st of 4 numbers) (DE-604)BV008000141 1144 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=029077582&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Moriwaki, Atsushi 1960- Adelic divisors on arithmetic varieties Memoirs of the American Mathematical Society |
| title | Adelic divisors on arithmetic varieties |
| title_auth | Adelic divisors on arithmetic varieties |
| title_exact_search | Adelic divisors on arithmetic varieties |
| title_full | Adelic divisors on arithmetic varieties Atsushi Moriwaki |
| title_fullStr | Adelic divisors on arithmetic varieties Atsushi Moriwaki |
| title_full_unstemmed | Adelic divisors on arithmetic varieties Atsushi Moriwaki |
| title_short | Adelic divisors on arithmetic varieties |
| title_sort | adelic divisors on arithmetic varieties |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=029077582&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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