Spectral theory and analytic geometry over non-Archimedean fields:
Saved in:
| Main Author: | |
|---|---|
| Other Authors: | |
| Format: | Book |
| Language: | English |
| Published: |
Providence, Rhode Island
American Mathematical Society
[1990]
|
| Series: | Mathematical Surveys and Monographs
Number 33 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | ix, 169 Seiten |
| ISBN: | 9780821890202 0821815342 |
Staff View
MARC
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| 100 | 1 | |a Berkovič, Vladimir G. |e Verfasser |0 (DE-588)1157343074 |4 aut | |
| 245 | 1 | 0 | |a Spectral theory and analytic geometry over non-Archimedean fields |c Vladimir G. Berkovich ; translated by Neal I. Koblitz |
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Record in the Search Index
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| adam_text | Contents
Introduction 1
Chapter 1. The Spectrum of a Commutative Banach Ring 11
1.1. Banach rings 11
1.2. The spectrum 12
1.3. Properties of the spectrum 15
1.4. Examples 17
1.5. Analytic spaces over a commutative Banach ring 19
Chapter 2. Affinoid Spaces 21
2.1. Affinoid algebras 21
2.2. Affinoid domains 27
2.3. Affinoid spaces 32
2.4. The reduction map 35
2.5. The relative interior 37
2.6. Functions analytic in a neighborhood of a closed subset 44
Chapter 3. Analytic Spaces 47
3.1. Definition and general properties 47
3.2. Topological properties of analytic spaces 52
3.3. Connection with rigid analytic geometry 56
3.4. GAGA: the case of nontrivial valuation 63
3.5. GAGA: the case of trivial valuation 68
3.6. Meromorphic functions 69
Chapter 4. Analytic Curves 75
4.1. One dimensional quasipolyhedra 75
4.2. The projective line 77
4.3. Curves of genus 1 81
4.4. Uniformization 85
4.5. Picard s Theorem 88
4.6. A characterization of curves whose Betti number is equal to the
genus 89
vii
viii CONTENTS
Chapter 5. Analytic Groups and Buildings 93
5.1. Subgroups and homogeneous spaces of analytic groups 93
5.2. Peaked points and the ^multiplication 97
5.3. A class of affinoid subgroups of a Chevalley group 103
5.4. Two embeddings of the building B{G) in Gan 108
5.5. Embeddings of the building 8{G) into compact
homogeneous spaces {G/H)an 111
Chapter 6. The Homotopy Type of Certain Analytic Spaces 115
6.1. Projective space and its subsets 115
6.2. Chevalley groups and their compact homogeneous spaces 118
6.3. Analytic tori 119
6.4. Analytic groups with potentially good reduction 121
6.5. Abelian varieties 124
6.6. Weak local contractibility of the two dimensional closed disc 125
Chapter 7. Spectral Theory 127
7.1. The spectrum and the resolvent 127
7.2. The spectrum with respect to a subalgebra 131
7.3. Holomorphie functional calculus 132
7.4. Partitions of the spectrum of an algebra 135
7.5. Partitions of the spectrum of an element 136
Chapter 8. Perturbation Theory 139
8.1. The Cauchy transform of a distribution with compact support 139
8.2. Fredholm theory 145
8.3. Perturbations of operators 148
8.4. The relative multiplicity of perturbation, and the trace formula 150
Chapter 9. The Dimension of a Banach Algebra 153
9.1. Dimension and stable dimension 153
9.2. Zero dimensional Banach algebras 155
9.3. Dimension of a subalgebra 158
References 161
Index 165
|
| any_adam_object | 1 |
| author | Berkovič, Vladimir G. |
| author2 | Koblitz, Neal 1948- |
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| author_GND | (DE-588)1157343074 (DE-588)108974820 |
| author_facet | Berkovič, Vladimir G. Koblitz, Neal 1948- |
| author_role | aut |
| author_sort | Berkovič, Vladimir G. |
| author_variant | v g b vg vgb |
| building | Verbundindex |
| bvnumber | BV043587165 |
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| classification_tum | MAT 144f MAT 320f |
| ctrlnum | (OCoLC)260220850 (DE-599)BVBBV043587165 |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV043587165 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:30:19Z |
| institution | BVB |
| isbn | 9780821890202 0821815342 |
| language | English |
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| physical | ix, 169 Seiten |
| publishDate | 1990 |
| publishDateSearch | 1990 |
| publishDateSort | 1990 |
| publisher | American Mathematical Society |
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| series | Mathematical Surveys and Monographs |
| series2 | Mathematical Surveys and Monographs |
| spelling | Berkovič, Vladimir G. Verfasser (DE-588)1157343074 aut Spectral theory and analytic geometry over non-Archimedean fields Vladimir G. Berkovich ; translated by Neal I. Koblitz Providence, Rhode Island American Mathematical Society [1990] © 1990 ix, 169 Seiten txt rdacontent n rdamedia nc rdacarrier Mathematical Surveys and Monographs Number 33 Spectral theory (Mathematics) Algebraic number theory Functional analysis Geometry, Analytic Algebraic number theory fast Functional analysis fast Geometry, Analytic fast Spectral theory (Mathematics) fast Analytische Geometrie (DE-588)4001867-2 gnd rswk-swf Nichtarchimedisch geordneter Körper (DE-588)4140076-8 gnd rswk-swf Spektraltheorie (DE-588)4116561-5 gnd rswk-swf Nichtarchimedisch geordneter Körper (DE-588)4140076-8 s DE-604 Spektraltheorie (DE-588)4116561-5 s Analytische Geometrie (DE-588)4001867-2 s Koblitz, Neal 1948- (DE-588)108974820 trl Erscheint auch als Online-Ausgabe 978-1-4704-1260-9 Mathematical Surveys and Monographs Number 33 (DE-604)BV000018014 33 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=029001687&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Berkovič, Vladimir G. Spectral theory and analytic geometry over non-Archimedean fields Mathematical Surveys and Monographs Spectral theory (Mathematics) Algebraic number theory Functional analysis Geometry, Analytic Algebraic number theory fast Functional analysis fast Geometry, Analytic fast Spectral theory (Mathematics) fast Analytische Geometrie (DE-588)4001867-2 gnd Nichtarchimedisch geordneter Körper (DE-588)4140076-8 gnd Spektraltheorie (DE-588)4116561-5 gnd |
| subject_GND | (DE-588)4001867-2 (DE-588)4140076-8 (DE-588)4116561-5 |
| title | Spectral theory and analytic geometry over non-Archimedean fields |
| title_auth | Spectral theory and analytic geometry over non-Archimedean fields |
| title_exact_search | Spectral theory and analytic geometry over non-Archimedean fields |
| title_full | Spectral theory and analytic geometry over non-Archimedean fields Vladimir G. Berkovich ; translated by Neal I. Koblitz |
| title_fullStr | Spectral theory and analytic geometry over non-Archimedean fields Vladimir G. Berkovich ; translated by Neal I. Koblitz |
| title_full_unstemmed | Spectral theory and analytic geometry over non-Archimedean fields Vladimir G. Berkovich ; translated by Neal I. Koblitz |
| title_short | Spectral theory and analytic geometry over non-Archimedean fields |
| title_sort | spectral theory and analytic geometry over non archimedean fields |
| topic | Spectral theory (Mathematics) Algebraic number theory Functional analysis Geometry, Analytic Algebraic number theory fast Functional analysis fast Geometry, Analytic fast Spectral theory (Mathematics) fast Analytische Geometrie (DE-588)4001867-2 gnd Nichtarchimedisch geordneter Körper (DE-588)4140076-8 gnd Spektraltheorie (DE-588)4116561-5 gnd |
| topic_facet | Spectral theory (Mathematics) Algebraic number theory Functional analysis Geometry, Analytic Analytische Geometrie Nichtarchimedisch geordneter Körper Spektraltheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=029001687&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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