Non-Archimedean analysis: a systematic approach to rigid analytic geometry
Gespeichert in:
| Hauptverfasser: | , , |
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[1984]
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| Schriftenreihe: | Grundlehren der mathematischen Wissenschaften
261 |
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| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Hier auch später erschienene, unveränderte Nachdrucke |
| Beschreibung: | XII, 436 Seiten |
| ISBN: | 3540125469 9783540125464 0387125469 9783642522314 |
Internformat
MARC
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| 020 | |a 9783540125464 |c hardcover |9 978-3-540-12546-4 | ||
| 020 | |a 0387125469 |c hardcover |9 0-387-12546-9 | ||
| 020 | |a 9783642522314 |c softcover |9 978-3-642-52231-4 | ||
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| 035 | |a (DE-599)BVBBV000169353 | ||
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| 100 | 1 | |a Bosch, Siegfried |d 1944- |e Verfasser |0 (DE-588)106950827 |4 aut | |
| 245 | 1 | 0 | |a Non-Archimedean analysis |b a systematic approach to rigid analytic geometry |c S. Bosch ; U. Güntzer ; R. Remmert |
| 264 | 1 | |a Berlin ; Heidelberg ; New York ; Tokyo |b Springer |c [1984] | |
| 264 | 4 | |c © 1984 | |
| 300 | |a XII, 436 Seiten | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Grundlehren der mathematischen Wissenschaften |v 261 | |
| 500 | |a Hier auch später erschienene, unveränderte Nachdrucke | ||
| 650 | 4 | |a Analyse fonctionnelle | |
| 650 | 4 | |a Géométrie analytique | |
| 650 | 7 | |a Niet-archimedische analyse |2 gtt | |
| 650 | 7 | |a Rigide analytische meetkunde |2 gtt | |
| 650 | 4 | |a Functional analysis | |
| 650 | 4 | |a Geometry, Analytic | |
| 650 | 0 | 7 | |a Analytische Geometrie |0 (DE-588)4001867-2 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Nichtarchimedische Analysis |0 (DE-588)4171709-0 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a p-adische Zahl |0 (DE-588)4044292-5 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Funktionalanalysis |0 (DE-588)4018916-8 |2 gnd |9 rswk-swf |
| 653 | 0 | |a Nichtarchimedische Analysis | |
| 653 | 0 | |a Affinoide Algebra | |
| 653 | 0 | |a Rigid-analytische Geometrie | |
| 653 | 0 | |a Analytische Geometrie | |
| 653 | 0 | |a Funktionalanalysis | |
| 689 | 0 | 0 | |a Analytische Geometrie |0 (DE-588)4001867-2 |D s |
| 689 | 0 | |5 DE-604 | |
| 689 | 1 | 0 | |a Funktionalanalysis |0 (DE-588)4018916-8 |D s |
| 689 | 1 | |5 DE-604 | |
| 689 | 2 | 0 | |a Nichtarchimedische Analysis |0 (DE-588)4171709-0 |D s |
| 689 | 2 | |5 DE-604 | |
| 689 | 3 | 0 | |a p-adische Zahl |0 (DE-588)4044292-5 |D s |
| 689 | 3 | 1 | |a Nichtarchimedische Analysis |0 (DE-588)4171709-0 |D s |
| 689 | 3 | |5 DE-604 | |
| 700 | 1 | |a Güntzer, Ulrich |d 1941- |e Verfasser |0 (DE-588)172109051 |4 aut | |
| 700 | 1 | |a Remmert, Reinhold |d 1930-2016 |e Verfasser |0 (DE-588)131654764 |4 aut | |
| 830 | 0 | |a Grundlehren der mathematischen Wissenschaften |v 261 |w (DE-604)BV000000395 |9 261 | |
| 856 | 4 | 2 | |m Digitalisierung UB Regensburg |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=000096431&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 940 | 1 | |q TUB-www | |
| 943 | 1 | |a oai:aleph.bib-bvb.de:BVB01-000096431 | |
Datensatz im Suchindex
| _version_ | 1805088108957401088 |
|---|---|
| adam_text |
Contents
Introduction
.
Part A. Linear Ultrametric Analysis and Valuation Theory
Chapter
1.
Norms and Valuations
. 9
1.1.
Semi-normed and normed groups
.
ÍI
1.1.1.
Ultrametric
f
unctions
. 9
1.1.2.
Filiations
. 11
1.1.3.
Semi-normed and normed groups. Ultrametric topology
. 11
1.1.4.
Distance
. 14
1.1.5.
Strictly closed subgroups
. 14
I.I.Ü.
Quotient groups
.
Hi
1.1.7.
Completions
. 17
1.1.8.
Convergent series
. 19
1.1.9.
Strict homomorphisms and completions
. 21
1.2.
Semi-normed and normed rings
. 23
1.2.1.
Semi-normed and normed rings
. 23
1.2.2.
Power-multiplicative and multiplicative elements
. 25
1.2.3.
The category
9І
and the functor A
—>
A~
. 26
1.2.4.
Topologically
nilpotent
elements and complete normed rings
. 26
1.2.5.
Power-bounded elements
. 28
1.3.
Power-multiplicative semi-norms
. 30
1.3.1.
Definition and elementary properties
. 30
1.3.2.
Smoothing procedures for semi-norms
. 32
1.3.3.
Standard examples of norms and semi-norms
. 34
1.4.
Strictly convergent power series
. 35
1.4.1.
Definition and structure of A(X)
. 35
1.4.2.
Structure of A{X)
. 37
1.4.3.
Bounded homomorphisms of A(X)
. 39
1.5.
Non-Archimedean valuations
. 41
1.5.1.
VTalued rings
. 41
1.5.2.
Examples
. 42
1.5.3.
The Gauss-Lemma
. 43
1.5.4.
Spectral value of monic polynomials
. 44
1.5.5.
Formal power series in countably many indeterminates
. 46
Vili
Contents
1.6.
Discrete
valuation rings
.
4s
1.0.1.
Definition. Elementary properties
. 48
1ЛІ.2.
The example of F. K. Schmidt
. 50
1.7.
Bald and discrete
Л
-rings.
52
1.7.1. ß-rings. 53
1.7.2.
Bald rings
. 54
1.8.
Quasi-Noetheriati .B-rings
. 55
1.8.1.
Definition and characterization
. 55
1.8.2.
Construction of quasi-Xoetherian rings
.
OU
Chapter
2.
Normed modules and normed vector spaces
. 03
2.1.
Xormed and faithfully narmed modules
. 03
2.1.1.
Definition
. 153
2.1.2.
.Submodules
and quotient modules
.
(Зо
2.1.3.
Modules of fractions. Completions
. 65
2.1.4.
Ramification index
.
6(>
2.1.5.
Direct sum. Bounded and restricted direct product
. 07
2.1.(5.
The module -V'(£,
M)
of bounded J-linear maps
. 69
2.1.7.
Complete tensor products
. 71
2.1.8.
Continuity and boundedness
. 77
2.1.9.
Density condition
. 80
2.1.10.
The functor
M
—
>J/~. Residue degree
. 81
2.2.
Examples of normed and faithfully normed
Л
-modules
.
82
2.2.1.
The module A"
. 82
2.2.2.
The modules Au\ A^K c(A) and b(A)
. 83
2.2.3.
Structure of
y(c¡(A),
M).
85
2.2.4.
The ring
Л
ЦІ',,
]"„.
.J
of formal power series
. 85
2.2.5.
6-separabIe modules
. 80
2.2.1).
The functor
M
~
»
T (M) .
87
2.3.
Weakly cartesian spaces
. 89
2.3.1.
Elementar}'
properties of normed spaces
. 90
2.3.2.
Weakly cartesian spaces
. 90
2.3.3.
Properties of weakly cartesian spaces
. 92
2.3.4.
Weakly cartesian spaces and tame modules
. 93
2.4.
('artesian spaces
. 94
2.4.1.
('artesian spaces of finite dimension
. 94
2.4.2.
Finite-dimensional cartesian spaces and strictly closed subspaces
. 96
2.4.3.
Cartesian spaces of arbitrary dimension
. 98
2.4.4.
Xormed vector spaces over a spherically complete field
. 102
2.5.
Strictly cartesian spaces
. 104
2.5.1.
Finite-dimensional strictly cartesian spaces
. 104
2.5.2.
Strictly cartesian spaces of arbitrary dimension
. 106
2.0.
Weakly cartesian spaces of countable dimension
. 107
2.(5.1.
Weakly cartesian bases
. 107
2.0.2.
Existence of weakly cartesian bases. Fundamental theorem
. 108
Contents
IX
2.7. Xormed
vector
spaces of countable type. The Lifting Theorem
.
HO
2.7.1.
Spaces of countable type
. 110
2.7.2. Schauder
bases. Orthogonality and orthonormality
. 114
2.7.3.
The Lifting Theorem
. 118
2.7.4.
Proof of the Lifting Theorem
. 119
2.7.5.
Applications
. 121
2.8.
Banach spaces
. 122
2.8.1.
Definition. Fundamental theorem
. 122
2.8.2.
Banach spaces of countable type
. 123
Chapter
íj.
Extensions of norms and valuations
. 125
3.1.
Xormed and faithfully normed algebras
. 125
3.1.1.
^-algebra norms
. 126
3.1.2.
Spectral values and power-multiplicative norms
. 129
3.1.3.
Residue degree and ramification index
. 130
3.1.4.
Dedekind's Lemma and a Finiteness Lemma
. 131
3.1.5.
Power-multiplicative and faithful
Л
-algebra
norms
. 133
3.2.
Algebraic field extensions. Spectral norm and valuations
. 134
3.2.1.
Spectral norm on algebraic field extensions
. 134
3.2.2.
Spectral norm on reduced integral A'-algebras
.
13tí
3.2.3.
Spectral norm and field polynomials
. 139
3.2.4.
Spectral norm and valuations
. 139
3.3.
Classical valuation theory
. 141
3.3.1.
Spectral norm and completions
. 141
3.3.2.
Construction of inequivalent valuations
. 141
3.3.3.
Construction of power-multiplicative algebra norms
. 142
3.3.4.
Hensel's Lemma
. 143
3.4.
Properties of the spectral valuation
. 145
3.4.1.
Continuity of roots
. 145
3.4.2.
Krasner's Lemma
. 148
3.4.3.
Example, p-adic numbers
. 149
3.5.
Weakly stable fields
. 151
3.5.1.
Weakly cartesian fields
. 151
3.5.2.
Weakly stable fields
. 152
3.5.3.
Criterion for weak stability
. 154
3.5.4.
Weak stability and
Japaneseness
. 155
3.6.
Stable fields
. 156
3.6.1.
Definition
. 156
3.6.2.
Criteria for stability
. 157
3.7.
Banach algebras
. 163
3.7.1.
Definition and examples
. 163
3.7.2.
Finiteness and completeness of modules over a Banach algebra
. 163
3.7.3.
The category
ША
. 164
3.7.4.
Finite homomorphisms
. 166
3.7.5.
Continuity of homomorphisms
. 167
X
Contents
3.8.
Function algebras
. 168
3.8.1.
The supremum semi-norm on ¿-algebras
. 168
3.8.2.
The supremum semi-norm on i-Banach algebras
. 174
3.8.3.
Banach function algebras
. 178
Chapter
4
(Appendix to Part A). Tame modules and Japanese rings
. 183
4.1.
Tame modules
. 183
4.2.
A Theorem of Dedekind
. 184
4.3.
Japanese rings. First criterion for
Japaneseness
. 185
4.4.
Tameness and
Japaneseness
. 186
Part B.
Aîïinoid
algebras
Chapter
ó.
Strictly
convergent
power series
. 191
5.1.
Definition and elementary properties of Tn and Tn
. 192
5.1.1.
Description of Tn
. 192
5.1.2.
The Gauss norm is a valuation and
Ťn
is a polynomial ring over
к
. . 193
5.1.3.
Going up and down between Tn and
Ťn
. 193
5.1.4.
Tn as a function algebra
. 196
5.2.
Weierstrass-
Rückert
theory for Tn
. 200
5.2.1.
Weierstrass
Division Theorem
. 200
5.2.2.
Weierstrass
Preparation Theorem
. 201
5.2.3.
Weierstrass
polynomials and
Weierstrass Finiteness
Theorem
. 202
5.2.4.
Generation of distinguished power series
. 204
5.2.5.
Riickert's theory
. 205
5.2.6.
Applications of Riickert's theory for Tn
. 207
5.2.7.
Finite ^„-modules
. 208
Õ.3.
.Stability of Q{Tn)
. 212
5.3.1.
Weak stability
. 212
5.3.2.
The Stability Theorem. Reductions
. 213
5.3.3.
Stability of
k(X)
if \k*\ is divisible
. 214
5.3.4.
Completion of the proof for arbitrary
1^*1. 218
Chapter
6.
А Шпоні
algebras and Piniteness Theorems
. 221
(i.l. Elementary properties of affinoid algebras
. 221
6.1.1.
The category
3Í
of ¿-affinoid algebras
. 221
6.1.2.
N"oet her normalization
. 227
6.1.3.
Continuity of homomorphisms
. 229
6.1.4.
Examples. Generalized rings of fractions
. 230
6.1.5.
Further examples. Convergent power series on general polydiscs
. . . 234
6.2.
The spectrum of a u-affinoid algebra and the supremum semi-norm
. 236
6.2.1.
The supremum semi-norm
. 236
6.2.2.
integral homomorphisms
. 238
6.2.3.
Power-bounded and topologically
nilpotent
elemente.
240
6.2.4.
Reduced
í-affinoid
algebras are Banaoh function algebras
. 242
Contents
XI
6.3.
The reduction functor A
·»->
A
. 242
6.3.1.
Monomorphisms, isometries and epimorphisms
. 243
6.3.2.
Finiteness of homomorphisms
. 245
6.3.3.
Applications to group operations
. 246
6.3.4.
Finiteness of the reduction functor A
-**■
A
. 247
6.3.5.
Summary
. 248
6.4.
The functor A ~
»
Å
. 249
6.4.1.
Finiteness Theorems
. 249
6.4.2.
Epimorphisms and isomorphisms
. 252
6.4.3.
Residue norm and supremum norm. Distinguished ¿-affinoid algebras
and epimorphisms
. 253
Part C. Rigid analytic geometry
Chapter
7.
Local theory of affinoid varieties
. 259
7.1.
Affinoid varieties
. 259
7.1.1.
Max Tn and the unit ball
Βη(^)
. 259
7.1.2.
Affinoid sets. Hubert's
Nullstellensatz . 262
7.1.3.
Closed subspaces of Max Tn
. 265
7.1.4.
Affinoid maps. The category of affinoid varieties
. 266
7.1.5.
The reduction functor
. 269
7.2.
Affinoid
subdomains
. 273
7.2.1.
The canonical topology on Sp A
. 273
7.2.2.
The universal property defining affinoid
subdomains
. 276
7.2.3.
Examples of open affinoid
subdomains
. 280
7.2.4.
Transitivity properties
. 284
7.2.5.
The Openness Theorem
. 287
7.2.6.
Affinoid
subdomains
and reduction
. 291
7.3.
Immersions of affinoid varieties
. 293
7.3.1.
Ideal-adic topologies
. 293
7.3.2.
Germs of affinoid functions
. 296
7.3.3.
Locally closed immersions
. 301
7.3.4. Runge
immersions
. 304
7.3.5.
Main theorem for locally closed immersions
. 309
Chapter
8.
Čech
eohomology of affinoid varieties
. 316
8.1.
Cech
eohomology with values in a presheaf
. 316
8.1.).
Cohomology of complexes
. 316
8.1.2.
Cohomology of double complexes
. 318
8.1.3.
Čech
cohomology
._. 320
8.1.4.
A Comparison Theorem for
Čech
cohomology
. 325
8.2.
Tate's Acyclicity Theorem
. 327
8.2.1.
Statement of the theorem
. 327
8.2.2.
Affinoid coverings
. 331
8.2.3.
Proof of the Acyclicity Theorem for Laurent coverings
. 334
XII Contents
Chapter
9.
Rigid analytic varieties
. . 336
9.1.
Grotiiendieck topologies
.
33b'
9.1.1.
rr-topological spaces
. 330
9.1.2.
Enhancing procedures for (/-topologies
. 338
9.1.3.
Pasting of
fť-topological
spaces
. 341
9.1.4.
(¿-topologies on affinoid varieties
. 342
9.2.
.Sheaf theory
. 346
9.2.1.
Preshea
ves
and sheaves on G'-topologieal spaces
. 346
9.2.2.
Sheafification of presheaves
. 348
9.2.3.
Extension of sheaves
. 352
9.3.
Analytic varieties. Definitions and constructions
. 353
9.3.1.
Locally (7-ringed spaces and analytic varieties
. 353
9.3.2.
Pasting of analytic varieties
. 358
9.3.3.
Pasting of analytic maps
. 360
9.3.4.
Some basic examples
. 301
îl.3.5.
Fibre products
. 365
9.3.6.
Extension of the ground field
. 368
9.4.
Coherent modules
. 371
9.4.1.
f
-modules
. 371
9.4.2.
Associated modules
. 373
9.4.3.
It-coherent modules
. 377
9.4.4.
Finite morphisms
. 382
9.5.
Closed analytic subvarieties
. 383
9.J.1. Coherent ideals. The nilradical
. 383
9.5.2.
Analytic subsets
. 385
9.5.3.
Closed immersions of analytic varieties
.
38S
9.6.
Separated and proper morphisms
. 391
9.6.1.
Separated morphisms
. 391
9.6.2.
Proper morphisms
. 394
9.6.3.
The Direct Image Theorem and the Theorem on Formal Functions
. . 396
9.7.
An application to elliptic curves
. 400
9.7.1.
Families of
annuii
. 400
9.7.2.
Affinoid
subdomains
of the unit disc
. 405
9.7.3.
Tate's elliptic curves
. 407
Bibliography
.416
Glossary of Notations
.421
Index
. .427 |
| any_adam_object | 1 |
| author | Bosch, Siegfried 1944- Güntzer, Ulrich 1941- Remmert, Reinhold 1930-2016 |
| author_GND | (DE-588)106950827 (DE-588)172109051 (DE-588)131654764 |
| author_facet | Bosch, Siegfried 1944- Güntzer, Ulrich 1941- Remmert, Reinhold 1930-2016 |
| author_role | aut aut aut |
| author_sort | Bosch, Siegfried 1944- |
| author_variant | s b sb u g ug r r rr |
| building | Verbundindex |
| bvnumber | BV000169353 |
| callnumber-first | Q - Science |
| callnumber-label | QA551 |
| callnumber-raw | QA551 |
| callnumber-search | QA551 |
| callnumber-sort | QA 3551 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 180 SK 380 SK 600 |
| classification_tum | MAT 144f MAT 127f MAT 307f |
| ctrlnum | (OCoLC)9644221 (DE-599)BVBBV000169353 |
| dewey-full | 516.3 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 516 - Geometry |
| dewey-raw | 516.3 |
| dewey-search | 516.3 |
| dewey-sort | 3516.3 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV000169353 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-20T09:02:48Z |
| institution | BVB |
| isbn | 3540125469 9783540125464 0387125469 9783642522314 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-000096431 |
| oclc_num | 9644221 |
| open_access_boolean | |
| owner | DE-12 DE-91G DE-BY-TUM DE-384 DE-703 DE-154 DE-739 DE-898 DE-BY-UBR DE-355 DE-BY-UBR DE-20 DE-824 DE-29T DE-19 DE-BY-UBM DE-706 DE-634 DE-83 DE-11 DE-188 |
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| physical | XII, 436 Seiten |
| psigel | TUB-www |
| publishDate | 1984 |
| publishDateSearch | 1984 |
| publishDateSort | 1984 |
| publisher | Springer |
| record_format | marc |
| series | Grundlehren der mathematischen Wissenschaften |
| series2 | Grundlehren der mathematischen Wissenschaften |
| spelling | Bosch, Siegfried 1944- Verfasser (DE-588)106950827 aut Non-Archimedean analysis a systematic approach to rigid analytic geometry S. Bosch ; U. Güntzer ; R. Remmert Berlin ; Heidelberg ; New York ; Tokyo Springer [1984] © 1984 XII, 436 Seiten txt rdacontent n rdamedia nc rdacarrier Grundlehren der mathematischen Wissenschaften 261 Hier auch später erschienene, unveränderte Nachdrucke Analyse fonctionnelle Géométrie analytique Niet-archimedische analyse gtt Rigide analytische meetkunde gtt Functional analysis Geometry, Analytic Analytische Geometrie (DE-588)4001867-2 gnd rswk-swf Nichtarchimedische Analysis (DE-588)4171709-0 gnd rswk-swf p-adische Zahl (DE-588)4044292-5 gnd rswk-swf Funktionalanalysis (DE-588)4018916-8 gnd rswk-swf Nichtarchimedische Analysis Affinoide Algebra Rigid-analytische Geometrie Analytische Geometrie Funktionalanalysis Analytische Geometrie (DE-588)4001867-2 s DE-604 Funktionalanalysis (DE-588)4018916-8 s Nichtarchimedische Analysis (DE-588)4171709-0 s p-adische Zahl (DE-588)4044292-5 s Güntzer, Ulrich 1941- Verfasser (DE-588)172109051 aut Remmert, Reinhold 1930-2016 Verfasser (DE-588)131654764 aut Grundlehren der mathematischen Wissenschaften 261 (DE-604)BV000000395 261 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=000096431&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Bosch, Siegfried 1944- Güntzer, Ulrich 1941- Remmert, Reinhold 1930-2016 Non-Archimedean analysis a systematic approach to rigid analytic geometry Grundlehren der mathematischen Wissenschaften Analyse fonctionnelle Géométrie analytique Niet-archimedische analyse gtt Rigide analytische meetkunde gtt Functional analysis Geometry, Analytic Analytische Geometrie (DE-588)4001867-2 gnd Nichtarchimedische Analysis (DE-588)4171709-0 gnd p-adische Zahl (DE-588)4044292-5 gnd Funktionalanalysis (DE-588)4018916-8 gnd |
| subject_GND | (DE-588)4001867-2 (DE-588)4171709-0 (DE-588)4044292-5 (DE-588)4018916-8 |
| title | Non-Archimedean analysis a systematic approach to rigid analytic geometry |
| title_auth | Non-Archimedean analysis a systematic approach to rigid analytic geometry |
| title_exact_search | Non-Archimedean analysis a systematic approach to rigid analytic geometry |
| title_full | Non-Archimedean analysis a systematic approach to rigid analytic geometry S. Bosch ; U. Güntzer ; R. Remmert |
| title_fullStr | Non-Archimedean analysis a systematic approach to rigid analytic geometry S. Bosch ; U. Güntzer ; R. Remmert |
| title_full_unstemmed | Non-Archimedean analysis a systematic approach to rigid analytic geometry S. Bosch ; U. Güntzer ; R. Remmert |
| title_short | Non-Archimedean analysis |
| title_sort | non archimedean analysis a systematic approach to rigid analytic geometry |
| title_sub | a systematic approach to rigid analytic geometry |
| topic | Analyse fonctionnelle Géométrie analytique Niet-archimedische analyse gtt Rigide analytische meetkunde gtt Functional analysis Geometry, Analytic Analytische Geometrie (DE-588)4001867-2 gnd Nichtarchimedische Analysis (DE-588)4171709-0 gnd p-adische Zahl (DE-588)4044292-5 gnd Funktionalanalysis (DE-588)4018916-8 gnd |
| topic_facet | Analyse fonctionnelle Géométrie analytique Niet-archimedische analyse Rigide analytische meetkunde Functional analysis Geometry, Analytic Analytische Geometrie Nichtarchimedische Analysis p-adische Zahl Funktionalanalysis |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=000096431&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000000395 |
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