Diophantine approximation and Abelian varieties: introductory lectures
Saved in:
| Format: | Book |
|---|---|
| Language: | English |
| Published: |
Berlin [u.a.]
Springer
1993
|
| Series: | Lecture notes in mathematics
1566 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XII, 127 S. |
| ISBN: | 3540575286 0387575286 |
Staff View
MARC
| LEADER | 00000nam a2200000 cb4500 | ||
|---|---|---|---|
| 001 | BV008313857 | ||
| 003 | DE-604 | ||
| 005 | 20080208 | ||
| 007 | t | ||
| 008 | 931025s1993 gw |||| 10||| eng d | ||
| 020 | |a 3540575286 |9 3-540-57528-6 | ||
| 020 | |a 0387575286 |9 0-387-57528-6 | ||
| 035 | |a (OCoLC)214565964 | ||
| 035 | |a (DE-599)BVBBV008313857 | ||
| 040 | |a DE-604 |b ger |e rakddb | ||
| 041 | 0 | |a eng | |
| 044 | |a gw |c DE | ||
| 049 | |a DE-384 |a DE-20 |a DE-12 |a DE-824 |a DE-29T |a DE-355 |a DE-91G |a DE-703 |a DE-19 |a DE-706 |a DE-634 |a DE-83 |a DE-11 |a DE-188 | ||
| 050 | 0 | |a QA3 | |
| 082 | 0 | |a 516.3/53 |2 20 | |
| 082 | 0 | |a 510 |2 20 | |
| 084 | |a SI 850 |0 (DE-625)143199: |2 rvk | ||
| 084 | |a SK 180 |0 (DE-625)143222: |2 rvk | ||
| 084 | |a MAT 102f |2 stub | ||
| 084 | |a MAT 147f |2 stub | ||
| 084 | |a 11Jxx |2 msc | ||
| 084 | |a 14Kxx |2 msc | ||
| 245 | 1 | 0 | |a Diophantine approximation and Abelian varieties |b introductory lectures |c B. Edixhoven ... (eds.) |
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 1993 | |
| 300 | |a XII, 127 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Lecture notes in mathematics |v 1566 | |
| 650 | 4 | |a Abelian varieties |x Congresses | |
| 650 | 4 | |a Diophantine approximation |x Congresses | |
| 650 | 0 | 7 | |a Abelsche Mannigfaltigkeit |0 (DE-588)4140992-9 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Diophantische Approximation |0 (DE-588)4135760-7 |2 gnd |9 rswk-swf |
| 655 | 7 | |0 (DE-588)1071861417 |a Konferenzschrift |2 gnd-content | |
| 689 | 0 | 0 | |a Abelsche Mannigfaltigkeit |0 (DE-588)4140992-9 |D s |
| 689 | 0 | 1 | |a Diophantische Approximation |0 (DE-588)4135760-7 |D s |
| 689 | 0 | |5 DE-604 | |
| 689 | 1 | 0 | |a Abelsche Mannigfaltigkeit |0 (DE-588)4140992-9 |D s |
| 689 | 1 | |5 DE-604 | |
| 689 | 2 | 0 | |a Diophantische Approximation |0 (DE-588)4135760-7 |D s |
| 689 | 2 | |5 DE-604 | |
| 700 | 1 | |a Edixhoven, Bas |d 1962- |e Sonstige |0 (DE-588)101493740X |4 oth | |
| 830 | 0 | |a Lecture notes in mathematics |v 1566 |w (DE-604)BV000676446 |9 1566 | |
| 856 | 4 | 2 | |m Digitalisierung TU Muenchen |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=005492614&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
Record in the Search Index
| _version_ | 1805082759597654016 |
|---|---|
| adam_text |
Contents
Preface
v
List of Contributors
ix
Introduction
x
Terminology and Prerequisites
xiii
I Diophantine Equations and Approximation,
by
F. Beukers
1
1
Heights
. 1
2
The Subspace Theorem
. 2
3
Weil Functions
. 5
4
Vojta's Conjecture
. 5
5
Results
. 9
II Diophantine Approximation and its Applications,
by R. TlJDEMAN
13
1
Upper Bounds for Approximations
. 13
2
Lower Bounds for Approximations
. 15
3
Applications to Diophantine Equations
. 17
III Roth's Theorem,
by R.
Tijdeman
21
1
The Proof
. 21
2
Variations and Generalisations
. 29
IV The Subspace Theorem of W.M. Schmidt,
by J.H. EVERTSE
31
1
Introduction
. 31
2
Applications
. 33
3
About the Proof of the Subspace theorem
. 37
V Heights on Abelian Varieties,
by J.
Huisman
51
1
Height on
Projective
Space
. 51
2
Heights on
Projective
Varieties
. 52
3
Heights on Abelian Varieties
. 55
4
Metrized Line Bundles
. 58
VI D. Mumford's "A Remark on Mordell's Conjecture",
by J. Top
63
1
Definitions
. 63
2
Mumford's Inequality
. 64
3
Interpretation, Consequences and an Example
. 64
4
The Proof assuming some Properties of Divisor Classes
. 65
5
Proof of the Divisorial Properties
. 66
6
Effectiveness and Generalizations
. 67
VII
Ample Line Bundles and Intersection Theory,
by A.J.
de Jong
69
1
Introduction
. 69
2
Coherent Sheaves, etc
. 69
3
Ample and Very Ample Line Bundles
. 71
4
Intersection Numbers
. 71
5
Numerical Equivalence and Ample Line Bundles
. 74
6
Lemmas to be used in the Proof of Thm. I of Faltings
. 75
Vm The Product Theorem,
by M. van
der
Рит
77
1
Differential Operators and Index
. 77
2
The Product Theorem
. 79
3
From the Product Theorem to Roth's Lemma
. 81
ГХ
Geometric Part of Faltings's Proof,
by C. Faber
83
X Faltings's Version of Siegel's Lemma,
by R.J. Kooman
93
XI Arithmetic Part of Faltings's Proof,
by B. Edixhoven
97
1
Introduction
.97
2
Construction of Proper Models
.97
3
Applying Faltings's version of Siegel's Lemma
.98
4
Leading Terms and Differential Operators
.103
5
Proof of the Main Theorem
.105
XII
Points of Degree
d
on Curves over Number Fields,
by G. van
der Geer
111
ХІП
"The" General Case of S. Lang's Conjecture (after Faltings),
by F. Oort
117
1
The Special Subset of a Variety
.117
2
The Special Subset of a Subvariety of an Abelian Variety
.119
3
The Arithmetic Case
.121
4
Related Conjectures and Results
.121
Bibliography
123 |
| any_adam_object | 1 |
| author_GND | (DE-588)101493740X |
| building | Verbundindex |
| bvnumber | BV008313857 |
| callnumber-first | Q - Science |
| callnumber-label | QA3 |
| callnumber-raw | QA3 |
| callnumber-search | QA3 |
| callnumber-sort | QA 13 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SI 850 SK 180 |
| classification_tum | MAT 102f MAT 147f |
| ctrlnum | (OCoLC)214565964 (DE-599)BVBBV008313857 |
| dewey-full | 516.3/53 510 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 516 - Geometry 510 - Mathematics |
| dewey-raw | 516.3/53 510 |
| dewey-search | 516.3/53 510 |
| dewey-sort | 3516.3 253 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>00000nam a2200000 cb4500</leader><controlfield tag="001">BV008313857</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">20080208</controlfield><controlfield tag="007">t</controlfield><controlfield tag="008">931025s1993 gw |||| 10||| eng d</controlfield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">3540575286</subfield><subfield code="9">3-540-57528-6</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">0387575286</subfield><subfield code="9">0-387-57528-6</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)214565964</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV008313857</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">rakddb</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="044" ind1=" " ind2=" "><subfield code="a">gw</subfield><subfield code="c">DE</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-384</subfield><subfield code="a">DE-20</subfield><subfield code="a">DE-12</subfield><subfield code="a">DE-824</subfield><subfield code="a">DE-29T</subfield><subfield code="a">DE-355</subfield><subfield code="a">DE-91G</subfield><subfield code="a">DE-703</subfield><subfield code="a">DE-19</subfield><subfield code="a">DE-706</subfield><subfield code="a">DE-634</subfield><subfield code="a">DE-83</subfield><subfield code="a">DE-11</subfield><subfield code="a">DE-188</subfield></datafield><datafield tag="050" ind1=" " ind2="0"><subfield code="a">QA3</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">516.3/53</subfield><subfield code="2">20</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">510</subfield><subfield code="2">20</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SI 850</subfield><subfield code="0">(DE-625)143199:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SK 180</subfield><subfield code="0">(DE-625)143222:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">MAT 102f</subfield><subfield code="2">stub</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">MAT 147f</subfield><subfield code="2">stub</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">11Jxx</subfield><subfield code="2">msc</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">14Kxx</subfield><subfield code="2">msc</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Diophantine approximation and Abelian varieties</subfield><subfield code="b">introductory lectures</subfield><subfield code="c">B. Edixhoven ... (eds.)</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Berlin [u.a.]</subfield><subfield code="b">Springer</subfield><subfield code="c">1993</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">XII, 127 S.</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="b">n</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="b">nc</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="490" ind1="1" ind2=" "><subfield code="a">Lecture notes in mathematics</subfield><subfield code="v">1566</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Abelian varieties</subfield><subfield code="x">Congresses</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Diophantine approximation</subfield><subfield code="x">Congresses</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Abelsche Mannigfaltigkeit</subfield><subfield code="0">(DE-588)4140992-9</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Diophantische Approximation</subfield><subfield code="0">(DE-588)4135760-7</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="655" ind1=" " ind2="7"><subfield code="0">(DE-588)1071861417</subfield><subfield code="a">Konferenzschrift</subfield><subfield code="2">gnd-content</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Abelsche Mannigfaltigkeit</subfield><subfield code="0">(DE-588)4140992-9</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2="1"><subfield code="a">Diophantische Approximation</subfield><subfield code="0">(DE-588)4135760-7</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="689" ind1="1" ind2="0"><subfield code="a">Abelsche Mannigfaltigkeit</subfield><subfield code="0">(DE-588)4140992-9</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="1" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="689" ind1="2" ind2="0"><subfield code="a">Diophantische Approximation</subfield><subfield code="0">(DE-588)4135760-7</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="2" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Edixhoven, Bas</subfield><subfield code="d">1962-</subfield><subfield code="e">Sonstige</subfield><subfield code="0">(DE-588)101493740X</subfield><subfield code="4">oth</subfield></datafield><datafield tag="830" ind1=" " ind2="0"><subfield code="a">Lecture notes in mathematics</subfield><subfield code="v">1566</subfield><subfield code="w">(DE-604)BV000676446</subfield><subfield code="9">1566</subfield></datafield><datafield tag="856" ind1="4" ind2="2"><subfield code="m">Digitalisierung TU Muenchen</subfield><subfield code="q">application/pdf</subfield><subfield code="u">http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=005492614&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA</subfield><subfield code="3">Inhaltsverzeichnis</subfield></datafield></record></collection> |
| genre | (DE-588)1071861417 Konferenzschrift gnd-content |
| genre_facet | Konferenzschrift |
| id | DE-604.BV008313857 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-20T07:37:46Z |
| institution | BVB |
| isbn | 3540575286 0387575286 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-005492614 |
| oclc_num | 214565964 |
| open_access_boolean | |
| owner | DE-384 DE-20 DE-12 DE-824 DE-29T DE-355 DE-BY-UBR DE-91G DE-BY-TUM DE-703 DE-19 DE-BY-UBM DE-706 DE-634 DE-83 DE-11 DE-188 |
| owner_facet | DE-384 DE-20 DE-12 DE-824 DE-29T DE-355 DE-BY-UBR DE-91G DE-BY-TUM DE-703 DE-19 DE-BY-UBM DE-706 DE-634 DE-83 DE-11 DE-188 |
| physical | XII, 127 S. |
| publishDate | 1993 |
| publishDateSearch | 1993 |
| publishDateSort | 1993 |
| publisher | Springer |
| record_format | marc |
| series | Lecture notes in mathematics |
| series2 | Lecture notes in mathematics |
| spelling | Diophantine approximation and Abelian varieties introductory lectures B. Edixhoven ... (eds.) Berlin [u.a.] Springer 1993 XII, 127 S. txt rdacontent n rdamedia nc rdacarrier Lecture notes in mathematics 1566 Abelian varieties Congresses Diophantine approximation Congresses Abelsche Mannigfaltigkeit (DE-588)4140992-9 gnd rswk-swf Diophantische Approximation (DE-588)4135760-7 gnd rswk-swf (DE-588)1071861417 Konferenzschrift gnd-content Abelsche Mannigfaltigkeit (DE-588)4140992-9 s Diophantische Approximation (DE-588)4135760-7 s DE-604 Edixhoven, Bas 1962- Sonstige (DE-588)101493740X oth Lecture notes in mathematics 1566 (DE-604)BV000676446 1566 Digitalisierung TU Muenchen application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=005492614&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Diophantine approximation and Abelian varieties introductory lectures Lecture notes in mathematics Abelian varieties Congresses Diophantine approximation Congresses Abelsche Mannigfaltigkeit (DE-588)4140992-9 gnd Diophantische Approximation (DE-588)4135760-7 gnd |
| subject_GND | (DE-588)4140992-9 (DE-588)4135760-7 (DE-588)1071861417 |
| title | Diophantine approximation and Abelian varieties introductory lectures |
| title_auth | Diophantine approximation and Abelian varieties introductory lectures |
| title_exact_search | Diophantine approximation and Abelian varieties introductory lectures |
| title_full | Diophantine approximation and Abelian varieties introductory lectures B. Edixhoven ... (eds.) |
| title_fullStr | Diophantine approximation and Abelian varieties introductory lectures B. Edixhoven ... (eds.) |
| title_full_unstemmed | Diophantine approximation and Abelian varieties introductory lectures B. Edixhoven ... (eds.) |
| title_short | Diophantine approximation and Abelian varieties |
| title_sort | diophantine approximation and abelian varieties introductory lectures |
| title_sub | introductory lectures |
| topic | Abelian varieties Congresses Diophantine approximation Congresses Abelsche Mannigfaltigkeit (DE-588)4140992-9 gnd Diophantische Approximation (DE-588)4135760-7 gnd |
| topic_facet | Abelian varieties Congresses Diophantine approximation Congresses Abelsche Mannigfaltigkeit Diophantische Approximation Konferenzschrift |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=005492614&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000676446 |
| work_keys_str_mv | AT edixhovenbas diophantineapproximationandabelianvarietiesintroductorylectures |