Rational points and arithmetic of fundamental groups: evidence for the section conjecture
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | German |
| Veröffentlicht: |
Berlin [u.a.]
Springer
2013
|
| Schriftenreihe: | Lecture notes in mathematics
2054 |
| Online-Zugang: | Volltext Inhaltsverzeichnis Abstract |
| Beschreibung: | Literaturangaben |
| Beschreibung: | 1 Online-Ressource (XX, 249 S.) |
| ISBN: | 9783642306747 |
| DOI: | 10.1007/978-3-642-30674-7 |
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Datensatz im Suchindex
| _version_ | 1804149640089567232 |
|---|---|
| adam_text | RATIONAL POINTS AND ARITHMETIC OF FUNDAMENTAL GROUPS
/ STIX, JAKOB
: 2013
TABLE OF CONTENTS / INHALTSVERZEICHNIS
PART I FOUNDATIONS OF SECTIONS
1 CONTINUOUS NON-ABELIAN H1 WITH PROFINITE COEFFICIENTS.-2 THE
FUNDAMENTAL GROUPOID
3 BASIC GEOMETRIC OPERATIONS IN TERMS OF SECTIONS
4 THE SPACE OF SECTIONS AS A TOPOLOGICAL SPACE
5 EVALUATION OF UNITS
6 CYCLE CLASSES IN ANABELIAN GEOMETRY
7 INJECTIVITY IN THE SECTION CONJECTURE
PART II BASIC ARITHMETIC OF SECTIONS
7 INJECTIVITY IN THE SECTION CONJECTURE
8 REDUCTION OF SECTIONS
9 THE SPACE OF SECTIONS IN THE ARITHMETIC CASE AND THE SECTION
CONJECTURE IN COVERS
PART III ON THE PASSAGE FROM LOCAL TO GLOBAL
10 LOCAL OBSTRUCTIONS AT A P-ADIC PLACE
11 BRAUER-MANIN AND DESCENT OBSTRUCTIONS
12 FRAGMENTS OF NON-ABELIAN TATE–POITOU DUALITY
PART IV ANALOGUES OF THE SECTION CONJECTURE
13 ON THE SECTION CONJECTURE FOR TORSORS
14 NILPOTENT SECTIONS
15 SECTIONS OVER FINITE FIELDS
16 ON THE SECTION CONJECTURE OVER LOCAL FIELDS
17 FIELDS OF COHOMOLOGICAL DIMENSION 1
18 CUSPIDAL SECTIONS AND BIRATIONAL ANALOGUES
DIESES SCHRIFTSTUECK WURDE MASCHINELL ERZEUGT.
RATIONAL POINTS AND ARITHMETIC OF FUNDAMENTAL GROUPS
/ STIX, JAKOB
: 2013
ABSTRACT / INHALTSTEXT
THE SECTION CONJECTURE IN ANABELIAN GEOMETRY, ANNOUNCED BY GROTHENDIECK
IN 1983, IS CONCERNED WITH A DESCRIPTION OF THE SET OF RATIONAL POINTS
OF A HYPERBOLIC ALGEBRAIC CURVE OVER A NUMBER FIELD IN TERMS OF THE
ARITHMETIC OF ITS FUNDAMENTAL GROUP. WHILE THE CONJECTURE IS STILL OPEN
TODAY IN 2012, ITS STUDY HAS REVEALED INTERESTING ARITHMETIC FOR CURVES
AND OPENED CONNECTIONS, FOR EXAMPLE, TO THE QUESTION WHETHER THE
BRAUER-MANIN OBSTRUCTION IS THE ONLY ONE AGAINST RATIONAL POINTS ON
CURVES. THIS MONOGRAPH BEGINS BY LAYING THE FOUNDATIONS FOR THE SPACE OF
SECTIONS OF THE FUNDAMENTAL GROUP EXTENSION OF AN ALGEBRAIC VARIETY.
THEN, ARITHMETIC ASSUMPTIONS ON THE BASE FIELD ARE IMPOSED AND THE
LOCAL-TO-GLOBAL APPROACH IS STUDIED IN DETAIL. THE MONOGRAPH CONCLUDES
BY DISCUSSING ANALOGUES OF THE SECTION CONJECTURE CREATED BY VARYING THE
BASE FIELD OR THE TYPE OF VARIETY, OR BY USING A CHARACTERISTIC QUOTIENT
OR ITS BIRATIONAL ANALOGUE IN LIEU OF THE FUNDAMENTAL GROUP EXTENSION
DIESES SCHRIFTSTUECK WURDE MASCHINELL ERZEUGT.
|
| any_adam_object | 1 |
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| discipline | Mathematik |
| doi_str_mv | 10.1007/978-3-642-30674-7 |
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| id | DE-604.BV040547488 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T00:26:14Z |
| institution | BVB |
| isbn | 9783642306747 |
| language | German |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-025393273 |
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| publisher | Springer |
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| series2 | Lecture notes in mathematics |
| spelling | Stix, Jakob 1974- Verfasser (DE-588)141161191 aut Rational points and arithmetic of fundamental groups evidence for the section conjecture Jakob Stix Berlin [u.a.] Springer 2013 1 Online-Ressource (XX, 249 S.) txt rdacontent c rdamedia cr rdacarrier Lecture notes in mathematics 2054 Literaturangaben Erscheint auch als Druck-Ausgabe, Paperback 978-3-642-30673-0 Lecture notes in mathematics 2054 (DE-604)BV014303148 2054 https://doi.org/10.1007/978-3-642-30674-7 Verlag Volltext Springer Fremddatenuebernahme application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025393273&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Springer Fremddatenuebernahme application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025393273&sequence=000003&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Abstract |
| spellingShingle | Stix, Jakob 1974- Rational points and arithmetic of fundamental groups evidence for the section conjecture Lecture notes in mathematics |
| title | Rational points and arithmetic of fundamental groups evidence for the section conjecture |
| title_auth | Rational points and arithmetic of fundamental groups evidence for the section conjecture |
| title_exact_search | Rational points and arithmetic of fundamental groups evidence for the section conjecture |
| title_full | Rational points and arithmetic of fundamental groups evidence for the section conjecture Jakob Stix |
| title_fullStr | Rational points and arithmetic of fundamental groups evidence for the section conjecture Jakob Stix |
| title_full_unstemmed | Rational points and arithmetic of fundamental groups evidence for the section conjecture Jakob Stix |
| title_short | Rational points and arithmetic of fundamental groups |
| title_sort | rational points and arithmetic of fundamental groups evidence for the section conjecture |
| title_sub | evidence for the section conjecture |
| url | https://doi.org/10.1007/978-3-642-30674-7 http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025393273&sequence=000001&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=025393273&sequence=000003&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA |
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