Lectures on formal and rigid geometry:
Gespeichert in:
| Beteilige Person: | |
|---|---|
| Format: | Buch |
| Sprache: | Englisch |
| Veröffentlicht: |
Cham [u.a.]
Springer
2014
|
| Schriftenreihe: | Lecture notes in mathematics
2105 |
| Schlagwörter: | |
| Links: | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027537744&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027537744&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA |
| Beschreibung: | Literaturverz. S. 249 - 250 |
| Umfang: | VIII, 254 S. graph. Darst. |
| ISBN: | 9783319044163 |
Internformat
MARC
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| 245 | 1 | 0 | |a Lectures on formal and rigid geometry |c Siegfried Bosch |
| 264 | 1 | |a Cham [u.a.] |b Springer |c 2014 | |
| 300 | |a VIII, 254 S. |b graph. Darst. | ||
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| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Lecture notes in mathematics |v 2105 | |
| 500 | |a Literaturverz. S. 249 - 250 | ||
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Datensatz im Suchindex
| DE-BY-TUM_call_number | 0102 MAT 001z 2001 B 999-2105 |
|---|---|
| DE-BY-TUM_katkey | 2029564 |
| DE-BY-TUM_location | 01 |
| DE-BY-TUM_media_number | 040071492885 |
| _version_ | 1821933913103138816 |
| adam_text | Contents
1
Introduction: Analytic Functions over
non-
Archimedean Fields
....... 1
Part I Classical Rigid Geometry
2
Tate
Algebras
................................................................. 9
2.1
Topology Induced from a Non-Archimedean Absolute Value
........ 9
2.2
Restricted Power Series
................................................. 12
2.3
Ideals in
Tate
Algebras
.................................................. 24
3
Affinoid Algebras and Their Associated Spaces
.......................... 31
3.1
Affinoid Algebras
....................................................... 31
3.2
Affinoid Spaces
......................................................... 42
3.3
Affinoid Subdomains
................................................... 45
4
Affinoid Functions
........................................................... 65
4.1
Germs of Affinoid Functions
........................................... 65
4.2
Locally Closed Immersions of Affinoid Spaces
....................... 69
4.3
Tate s
Acyclicity
Theorem
.............................................. 82
5
Towards the Notion of Rigid Spaces
....................................... 93
5.1
Grothendieck Topologies
............................................... 93
5.2
Sheaves
.................................................................. 99
5.3
Rigid Spaces
............................................................. 103
5.4
The GAGA-Functor
..................................................... 109
6
Coherent Sheaves on Rigid Spaces
......................................... 117
6.1
Coherent Modules
....................................................... 117
6.2
Grothendieck Cohomology
............................................. 125
6.3
The Proper Mapping Theorem
......................................... 129
6.4
Proof of the Proper Mapping Theorem
................................ 133
vu
viii Contents
Part II Formal Geometry
7
Adic
Rings and Their Associated Formal Schemes
...................... 151
7.1
Adic
Rings
............................................................... 151
7.2
Formal Schemes
......................................................... 158
7.3
Algebras of Topologically Finite Type
................................. 162
7.4
Admissible Formal Schemes
........................................... 169
8
Raynaud s View on Rigid Spaces
........................................... 175
8.1
Coherent Modules
....................................................... 175
8.2
Admissible Formal Blowing-Up
....................................... 179
8.3
Rig-Points in the Classical Rigid Setting
.............................. 194
8.4
Rigid Spaces in Terms of Formal Models
.............................. 202
9
More Advanced Stuff
........................................................ 215
9.1
Relative Rigid Spaces
................................................... 215
9.2
An Example: Raynaud s Universal
Tate
Curve
........................ 217
9.3
The Zariski-Riemann Space
............................................ 220
9.4
Further Results on Formal Models
..................................... 223
Appendix A: Classical Valuation Theory
...................................... 229
Appendix B: Completed Tensor Products
..................................... 237
References
......................................................................... 249
Index
............................................................................... 251
Lecture
Notes
in Mathematics
2105
Siegfried Bosch
Lectures on Formal and Rigid Geometry
A first version of this work appeared in
2005
as a Preprint of the Collaborative
Research Center Geometrical Structures in Mathematics at the University of
Münster.
Its aim was to offer a concise and self-contained lecture-style introduction
to the theory of classical rigid geometry established by John
Tate,
together with the
formal algebraic geometry approach launched by Michel Raynaud. These Lectures
are now viewed commonly as an ideal means of learning advanced rigid geometry,
regardless of the reader s level of background. Despite its parsimonious style, the
presentation illustrates a number of key facts even more extensively than any other
previous work.
This Lecture Notes Volume is a revised and slightly expanded version of the original
preprint and has been published at the suggestion of several experts in the field.
|
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| classification_rvk | SI 850 SK 180 |
| classification_tum | MAT 140f |
| ctrlnum | (OCoLC)894662747 (DE-599)BSZ401084418 |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV042096993 |
| illustrated | Illustrated |
| indexdate | 2024-12-20T17:02:12Z |
| institution | BVB |
| isbn | 9783319044163 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-027537744 |
| oclc_num | 894662747 |
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| owner_facet | DE-188 DE-83 DE-91G DE-BY-TUM DE-824 DE-355 DE-BY-UBR DE-11 DE-706 |
| physical | VIII, 254 S. graph. Darst. |
| publishDate | 2014 |
| publishDateSearch | 2014 |
| publishDateSort | 2014 |
| publisher | Springer |
| record_format | marc |
| series | Lecture notes in mathematics |
| series2 | Lecture notes in mathematics |
| spellingShingle | Bosch, Siegfried 1944- Lectures on formal and rigid geometry Lecture notes in mathematics Algebraische Geometrie (DE-588)4001161-6 gnd |
| subject_GND | (DE-588)4001161-6 |
| title | Lectures on formal and rigid geometry |
| title_auth | Lectures on formal and rigid geometry |
| title_exact_search | Lectures on formal and rigid geometry |
| title_full | Lectures on formal and rigid geometry Siegfried Bosch |
| title_fullStr | Lectures on formal and rigid geometry Siegfried Bosch |
| title_full_unstemmed | Lectures on formal and rigid geometry Siegfried Bosch |
| title_short | Lectures on formal and rigid geometry |
| title_sort | lectures on formal and rigid geometry |
| topic | Algebraische Geometrie (DE-588)4001161-6 gnd |
| topic_facet | Algebraische Geometrie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027537744&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027537744&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000676446 |
| work_keys_str_mv | AT boschsiegfried lecturesonformalandrigidgeometry |
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Teilbibliothek Mathematik & Informatik
| Signatur: |
0102 MAT 001z 2001 B 999-2105 Lageplan |
|---|---|
| Exemplar 1 | Ausleihbar Am Standort |