Arithmetic geometry: lectures given at the C.I.M.E. Summer School held in Cetraro, Italy, September 10 - 15, 2007
Gespeichert in:
| Weitere Verfasser: | |
|---|---|
| Format: | Tagungsbericht Buch |
| Sprache: | English French |
| Veröffentlicht: |
Berlin [u.a.]
Springer
2011
|
| Schriftenreihe: | Lecture notes in mathematics
2009 |
| Schlagworte: | |
| Online-Zugang: | Inhaltstext Inhaltsverzeichnis |
| Beschreibung: | XI, 232 S. 235 mm x 155 mm |
| ISBN: | 9783642159442 |
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| 245 | 1 | 0 | |a Arithmetic geometry |b lectures given at the C.I.M.E. Summer School held in Cetraro, Italy, September 10 - 15, 2007 |c Jean-Louis Colliot-Thélène ; Peter Swinnerton-Dyer ; Paul Vojta. Eds.: Pietro Corvaja ... |
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Datensatz im Suchindex
| _version_ | 1805095073715585024 |
|---|---|
| adam_text |
IMAGE 1
CONTENTS
VARIETES PRESQUE RATIONNELLES, LEURS POINTS RATIONNELS ET LEURS
DEGENERESCENCES 1
JEAN-LOUIS COLLIOT-THELENE 1 INTRODUCTION 1
2 NOTATIONS, RAPPELS ET PRELIMINAIRES 2
3 SCHEMAS AU-DESSUS D'UN ANNEAU DE VALUATION DISCRETE 4
3.1 /4-SCHEMAS DE TYPE (R), CROISEMENTS NORMAUX, CROISEMENTS NORMAUX
STRICTS 4
3.2 QUAND LA FIBRE SPECIALE A UNE COMPOSANTE DE MULTIPLICITE 1 5
3.3 QUAND LA FIBRE SPECIALE CONTIENT UNE SOUS-VARIETE GEOMETRIQUEMENT
INTEGRE 6
3.4 QUAND LA FIBRE SPECIALE A UNE COMPOSANTE GEOMETRIQUEMENT INTEGRE DE
MULTIPLICITE 1 7
3.5 UN EXEMPLE : QUADRIQUES 9
4 GROUPE DE BRAUER DES SCHEMAS AU-DESSUS D'UN ANNEAU DE VALUATION
DISCRETE 10
5 CORPSC, 12
6 /?-EQUIVALENCE ET EQUIVALENCE RATIONNELLE SUR LES ZERO-CYCLES 14 7
AUTOUR DU THEOREME DE TSEN : VARIETES RATIONNELLEMENT CONNEXES 14 8
AUTOUR DU THEOREME DE CHEVALLEY-WARNING : VARIETES DONT LE GROUPE DE
CHOW GEOMETRIQUE EST TRIVIAL 21
9 APPROXIMATION FAIBLE POUR LES VARIETES RATIONNELLEMENT CONNEXES 22 10
^-EQUIVALENCE SUR LES VARIETES RATIONNELLEMENT CONNEXES 23 11
EQUIVALENCE RATIONNELLE SUR LES ZERO-CYCLES DES VARIETES RATIONNELLEMENT
CONNEXES 27
12 VERS LES VARIETES SUPERIEUREMENT RATIONNELLEMENT CONNEXES 29 12.1
DEUX EXEMPLES 29
12.2 FIBRES SPECIALES AVEC UNE COMPOSANTE GEOMETRIQUEMENT INTEGRE DE
MULTIPLICITE 1 30
12.3 VARIETES RATIONNELLEMENT SIMPLEMENT CONNEXES 32
12.4 EXISTENCE D'UN POINT RATIONNEL SUR UN CORPS DE FONCTIONS DE DEUX
VARIABLES 34
BIBLIOGRAFISCHE INFORMATIONEN HTTP://D-NB.INFO/1005647046
DIGITALISIERT DURCH
IMAGE 2
X CONTENTS
12.5 APPROXIMATION FAIBLE EN TOUTES LES PLACES D'UN CORPS DE FONCTIONS
D'UNE VARIABLE 35
12.6 /F-EQUIVALENCE ET EQUIVALENCE RATIONNELLE 36
13 SURJECTIVITE ARITHMETIQUE ET SURJECTIVITE GEOMETRIQUE 37
13.1 MORPHISMES DEFINIS SUR UN CORPS DE NOMBRES ET APPLICATIONS INDUITES
SUR LES POINTS LOCAUX 38
13.2 QUELQUES AUTRES QUESTIONS 40
BIBLIOGRAPHIE 41
TOPICS IN DIOPHANTINE EQUATIONS 45
SIR PETER SWINNERTON-DYER 1 INTRODUCTION 45
2 THE HASSE PRINCIPLE AND THE BRAUER-MANIN OBSTRUCTION 47
3 ZETA-FUNCTIONS AND L-SERIES 52
4 CURVES 55
5 VARIETIES OF HIGHER DIMENSION AND THE HARDY-LITTLEWOOD METHOD 58 6
MANIN'S CONJECTURE 60
7 SCHINZEL'S HYPOTHESIS AND SALBERGER'S DEVICE 65
8 THE LEGENDRE-JACOBI FUNCTION 69
9 PENCILS OF CONIES 75
10 2-DESCENT ON ELLIPTIC CURVES 80
11 PENCILS OF CURVES OF GENUS 1 86
12 SOME EXAMPLES 93
12.1 DIAGONAL QUARTIC SURFACES 93
12.2 SOME KUMMER SURFACES 98
12.3 DIAGONAL CUBIC SURFACES 98
13 THE CASE OF ONE RATIONAL 2-DIVISION POINT 101
14 DEL PEZZO SURFACES OF DEGREE 4 105
REFERENCES 108
DIOPHANTINE APPROXIMATION AND NEVANLINNA THEORY ILL
PAUL VOJTA 1 INTRODUCTION ILL
2 NOTATION AND BASIC RESULTS: NUMBER THEORY 113
3 HEIGHTS 115
4 ROTH'S THEOREM 117
5 BASICS OF NEVANLINNA THEORY 120
6 ROTH'S THEOREM AND NEVANLINNA THEORY 123
7 THE DICTIONARY (NON-GEOMETRIC CASE) 127
8 CARTAN'S THEOREM AND SCHMIDT'S SUBSPACE THEOREM 130
9 VARIETIES AND WEIL FUNCTIONS 134
10 HEIGHT FUNCTIONS ON VARIETIES IN NUMBER THEORY 140
11 PROXIMITY AND COUNTING FUNCTIONS ON VARIETIES IN NUMBER THEORY 145 12
HEIGHT, PROXIMITY, AND COUNTING FUNCTIONS IN NEVANLINNA THEORY 147 13
INTEGRAL POINTS 151
IMAGE 3
CONTENTS XI
14 UNITS AND THE BOREL LEMMA 154
15 CONJECTURES IN NEVANLINNA THEORY AND NUMBER THEORY 155 16 FUNCTION
FIELDS 160
17 THE EXCEPTIONAL SET 163
18 COMPARISON OF PROBLEM TYPES 165
19 EMBEDDINGS 166
20 SCHMIDT'S SUBSPACE THEOREM IMPLIES SIEGEL'S THEOREM 169 21 THE
CORVAJA-ZANNIER METHOD IN HIGHER DIMENSIONS 170
22 WORKOFEVERTSEANDFERRETTI 177
23 TRUNCATED COUNTING FUNCTIONS AND THE ABC CONJECTURE 185 24 ON
DISCRIMINANTS 190
25 A DIOPHANTINE CONJECTURE FOR ALGEBRAIC POINTS 198
26 THE 1 +E CONJECTURE AND THE ABC CONJECTURE 200
27 NEVANLINNA THEORY OF FINITE RAMIFIED COVERINGS 201
28 THE 1 +E CONJECTURE IN THE SPLIT FUNCTION FIELD CASE 204
29 DERIVATIVES IN NEVANLINNA THEORY 206
30 DERIVATIVES IN NUMBER THEORY 212
31 ANOTHER CONJECTURE IMPLIES ABC 215
32 AN ABC IMPLICATION IN THE OTHER DIRECTION 217
REFERENCES 220
INDEX 225 |
| any_adam_object | 1 |
| author2 | Corvaja, Pietro 1967- |
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| author_facet | Corvaja, Pietro 1967- |
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| bvnumber | BV036850560 |
| classification_rvk | SI 850 |
| classification_tum | MAT 144f MAT 102f |
| ctrlnum | (OCoLC)690908585 (DE-599)DNB1005647046 |
| dewey-full | 516.35 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 516 - Geometry |
| dewey-raw | 516.35 |
| dewey-search | 516.35 |
| dewey-sort | 3516.35 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Conference Proceeding Book |
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| illustrated | Not Illustrated |
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| series2 | Lecture notes in mathematics |
| spelling | Arithmetic geometry lectures given at the C.I.M.E. Summer School held in Cetraro, Italy, September 10 - 15, 2007 Jean-Louis Colliot-Thélène ; Peter Swinnerton-Dyer ; Paul Vojta. Eds.: Pietro Corvaja ... Berlin [u.a.] Springer 2011 XI, 232 S. 235 mm x 155 mm txt rdacontent n rdamedia nc rdacarrier Lecture notes in mathematics 2009 Arithmetische Geometrie (DE-588)4131383-5 gnd rswk-swf (DE-588)1071861417 Konferenzschrift 2007 Cetraro gnd-content Arithmetische Geometrie (DE-588)4131383-5 s DE-604 Colliot-Thélène, Jean-Louis 1947- Sonstige (DE-588)11022065X oth Swinnerton-Dyer, Henry P. F. 1927-2018 Sonstige (DE-588)114274185 oth Vojta, Paul 1957- Sonstige (DE-588)111319668 oth Corvaja, Pietro 1967- (DE-588)142972576 edt Summer School Arithmetic Geometry 2007 Cetraro Sonstige (DE-588)16171243-5 oth Erscheint auch als Online-Ausgabe 978-3-642-15945-9 Lecture notes in mathematics 2009 (DE-604)BV000676446 2009 X:MVB text/html http://deposit.dnb.de/cgi-bin/dokserv?id=3523484&prov=M&dok_var=1&dok_ext=htm Inhaltstext DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020766535&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Arithmetic geometry lectures given at the C.I.M.E. Summer School held in Cetraro, Italy, September 10 - 15, 2007 Lecture notes in mathematics Arithmetische Geometrie (DE-588)4131383-5 gnd |
| subject_GND | (DE-588)4131383-5 (DE-588)1071861417 |
| title | Arithmetic geometry lectures given at the C.I.M.E. Summer School held in Cetraro, Italy, September 10 - 15, 2007 |
| title_auth | Arithmetic geometry lectures given at the C.I.M.E. Summer School held in Cetraro, Italy, September 10 - 15, 2007 |
| title_exact_search | Arithmetic geometry lectures given at the C.I.M.E. Summer School held in Cetraro, Italy, September 10 - 15, 2007 |
| title_full | Arithmetic geometry lectures given at the C.I.M.E. Summer School held in Cetraro, Italy, September 10 - 15, 2007 Jean-Louis Colliot-Thélène ; Peter Swinnerton-Dyer ; Paul Vojta. Eds.: Pietro Corvaja ... |
| title_fullStr | Arithmetic geometry lectures given at the C.I.M.E. Summer School held in Cetraro, Italy, September 10 - 15, 2007 Jean-Louis Colliot-Thélène ; Peter Swinnerton-Dyer ; Paul Vojta. Eds.: Pietro Corvaja ... |
| title_full_unstemmed | Arithmetic geometry lectures given at the C.I.M.E. Summer School held in Cetraro, Italy, September 10 - 15, 2007 Jean-Louis Colliot-Thélène ; Peter Swinnerton-Dyer ; Paul Vojta. Eds.: Pietro Corvaja ... |
| title_short | Arithmetic geometry |
| title_sort | arithmetic geometry lectures given at the c i m e summer school held in cetraro italy september 10 15 2007 |
| title_sub | lectures given at the C.I.M.E. Summer School held in Cetraro, Italy, September 10 - 15, 2007 |
| topic | Arithmetische Geometrie (DE-588)4131383-5 gnd |
| topic_facet | Arithmetische Geometrie Konferenzschrift 2007 Cetraro |
| url | http://deposit.dnb.de/cgi-bin/dokserv?id=3523484&prov=M&dok_var=1&dok_ext=htm http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020766535&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000676446 |
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