Geometric modular forms and elliptic curves:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Singapore [u.a.]
World Scientific
2000
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | X, 361 S. |
| ISBN: | 9810243375 |
Internformat
MARC
| LEADER | 00000nam a2200000 c 4500 | ||
|---|---|---|---|
| 001 | BV013791237 | ||
| 003 | DE-604 | ||
| 005 | 00000000000000.0 | ||
| 007 | t | ||
| 008 | 010627s2000 |||| 00||| eng d | ||
| 020 | |a 9810243375 |9 981-02-4337-5 | ||
| 035 | |a (OCoLC)44046812 | ||
| 035 | |a (DE-599)BVBBV013791237 | ||
| 040 | |a DE-604 |b ger |e rakwb | ||
| 041 | 0 | |a eng | |
| 049 | |a DE-20 |a DE-355 |a DE-824 |a DE-11 |a DE-384 | ||
| 050 | 0 | |a QA567.2.E44 | |
| 082 | 0 | |a 516.3/52 |2 21 | |
| 084 | |a SK 240 |0 (DE-625)143226: |2 rvk | ||
| 100 | 1 | |a Hida, Haruzo |d 1952- |e Verfasser |0 (DE-588)129238260 |4 aut | |
| 245 | 1 | 0 | |a Geometric modular forms and elliptic curves |c Haruzo Hida |
| 264 | 1 | |a Singapore [u.a.] |b World Scientific |c 2000 | |
| 300 | |a X, 361 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 650 | 4 | |a Courbes elliptiques | |
| 650 | 7 | |a Curvas eliticas |2 larpcal | |
| 650 | 7 | |a Elliptische oppervlakken |2 gtt | |
| 650 | 4 | |a Formes modulaires | |
| 650 | 7 | |a Geometria algébrica |2 larpcal | |
| 650 | 7 | |a Vormen (wiskunde) |2 gtt | |
| 650 | 4 | |a Curves, Elliptic | |
| 650 | 4 | |a Forms, Modular | |
| 650 | 0 | 7 | |a Modulraum |0 (DE-588)4183462-8 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Elliptische Kurve |0 (DE-588)4014487-2 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Elliptische Kurve |0 (DE-588)4014487-2 |D s |
| 689 | 0 | 1 | |a Modulraum |0 (DE-588)4183462-8 |D s |
| 689 | 0 | |5 DE-604 | |
| 856 | 4 | 2 | |m HBZ Datenaustausch |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009428378&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-009428378 | ||
Datensatz im Suchindex
| _version_ | 1804128614330925056 |
|---|---|
| adam_text | Contents
Preface v
Chapter 1 An Algebro-Geometric Tool Box 1
1.1 Sheaves 1
1.1.1 Sheaves and Presheaves 1
1.1.2 Sheafication 2
1.1.3 Sheaf Kernel and Cokernel 4
1.2 Schemes 5
1.2.1 Local Ringed Spaces 5
1.2.2 Schemes as Local Ringed Spaces 8
1.2.3 Sheaves over Schemes 9
1.2.4 Topological Properties of Schemes 11
1.3 Projective Schemes 13
1.3.1 Graded Rings 13
1.3.2 Functor Proj 13
1.3.3 Sheaves on Projective Schemes 17
1.4 Categories and Functors 20
1.4.1 Categories 21
1.4.2 Functors 22
1.4.3 Schemes as Functors 23
1.4.4 Abelian Categories 25
1.5 Applications of the Key-Lemma 28
1.5.1 Sheaf of Differential Forms on Schemes 28
1.5.2 Fiber Products 31
1.5.3 Inverse Image of Sheaves 32
1.5.4 Affine Schemes 35
vii
viii Contents
1.5.5 Morphisms into a Projective Space 36
1.6 Group Schemes 37
1.6.1 Group Schemes as Functors 37
1.6.2 Kernel and Cokernel 39
1.6.3 Bialgebras 40
1.6.4 Locally Free Groups 42
1.6.5 Schematic Representations 44
1.7 Cartier Duality 45
1.7.1 Duality of Bialgebras 45
1.7.2 Duality of Locally Free Groups 47
1.8 Quotients by a Group Scheme 50
1.8.1 Naive Quotients 50
1.8.2 Categorical Quotients 52
1.8.3 Geometric Quotients 54
1.9 Morphisms 62
1.9.1 Topological Definitions 62
1.9.2 Diffeo-Geometric Definitions 67
1.9.3 Applications 69
1.10 Cohomology of Coherent Sheaves 72
1.10.1 Coherent Cohomology 73
1.10.2 Summary of Known Facts 77
1.10.3 Cohomological Dimension 79
1.11 Descent 82
1.11.1 Covering Data 82
1.11.2 Descent Data 84
1.11.3 An Application to Schemes 86
Chapter 2 Elliptic Curves 89
2.1 Curves and Divisors 89
2.1.1 Cartier Divisors 89
2.1.2 Grothendieck-Serre Duality 93
2.1.3 Riemann-Roch Theorem 98
2.1.4 Relative Riemann-Roch Theorem 103
2.2 Elliptic Curves 107
2.2.1 Definition 107
2.2.2 Abel s Theorem 108
2.2.3 Holomorphic Differentials 110
2.2.4 Taylor Expansion of Differentials Ill
2.2.5 Weierstrass Equations of Elliptic Curves 112
Contents ix
2.2.6 Moduli of Weierstrass Type 115
2.3 Geometric Modular Forms of Level 1 119
2.3.1 Functorial Definition 119
2.3.2 Coarse Moduli Scheme 120
2.3.3 Fields of Moduli 123
2.4 Elliptic Curves over C 124
2.4.1 Topological Fundamental Groups 125
2.4.2 Classical Weierstrass Theory 127
2.4.3 Complex Modular Forms 128
2.5 Elliptic Curves over p-Adic Fields 130
2.5.1 Power Series Identities 130
2.5.2 Universal Tate Curves 133
2.5.3 Etale Covering of Tate Curves 138
2.6 Level Structures 140
2.6.1 Isogenies 140
2.6.2 Level N Moduli Problems 143
2.6.3 Generality of Elliptic Curves 149
2.6.4 Proof of Theorem 2.6.8 151
2.6.5 Geometric Modular Forms of Level N 154
2.7 L-Functions of Elliptic Curves 160
2.7.1 L-Functions over Finite Fields 160
2.7.2 Hasse-Weil L-Function 162
2.8 Regularity 166
2.8.1 Regular Rings 167
2.8.2 Regular Moduli Varieties 170
2.9 p-Ordinary Moduli Problems 175
2.9.1 The Hasse Invariant 176
2.9.2 Ordinary Moduli of p-Power Level 179
2.9.3 Irreducibility of p-Ordinary Moduli 182
2.9.4 Moduli Problem of Fo and I Type 183
2.9.5 Moduli Problem of ro(p) and Ti(p) Type 185
Chapter 3 Geometric Modular Forms 197
3.1 Integrality 197
3.1.1 Spaces of Modular Forms 197
3.1.2 Horizontal Control Theorem 210
3.2 Vertical Control Theorem 212
3.2.1 False Modular Forms 214
3.2.2 p-Adic Modular Forms 227
x Contents
3.2.3 Hecke Operators 232
3.2.4 Families of p-Adic Modular Forms 239
3.2.5 Horizontal Control of p-Power Level 244
3.3 Action of GL(2) on Modular Forms 246
3.3.1 Action of GL2(1/NZ) 246
3.3.2 Action of GL2(Z) 250
Chapter 4 Jacobians and Galois Representations 257
4.1 Jacobians of Stable Curves 257
4.1.1 Non-Singular Curves 257
4.1.2 Union of Two Curves 265
4.1.3 Functorial Properties of Jacobians 268
4.1.4 Self-Duality of Jacobian Schemes 272
4.1.5 Generality on Abelian Schemes 274
4.1.6 Endomorphism of Abelian Schemes 283
4.1.7 ^-Adic Galois Representations 288
4.2 Modular Galois Representations 292
4.2.1 Hecke Correspondences 293
4.2.2 Galois Representations on Modular Jacobians 296
4.2.3 Ramification at the Level 300
4.2.4 Ramification of p-Adic Representations at p 306
4.2.5 Modular Galois Representations of Higher Weight . . . 308
Chapter 5 Modularity Problems 313
5.1 Induced and Extended Galois Representations 314
5.1.1 Induction and Extension 314
5.1.2 Automorphic Induction 322
5.1.3 Artin Representations 325
5.2 Some Other Solutions 331
5.2.1 A Theorem of Wiles 331
5.2.2 Modularity of Extended Galois Representations 333
5.2.3 Elliptic Q-Curves 336
5.2.4 Shimura-Taniyama Conjecture 343
Bibliography 347
List of Symbols 355
List of Statements 357
Index 359
|
| any_adam_object | 1 |
| author | Hida, Haruzo 1952- |
| author_GND | (DE-588)129238260 |
| author_facet | Hida, Haruzo 1952- |
| author_role | aut |
| author_sort | Hida, Haruzo 1952- |
| author_variant | h h hh |
| building | Verbundindex |
| bvnumber | BV013791237 |
| callnumber-first | Q - Science |
| callnumber-label | QA567 |
| callnumber-raw | QA567.2.E44 |
| callnumber-search | QA567.2.E44 |
| callnumber-sort | QA 3567.2 E44 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 240 |
| ctrlnum | (OCoLC)44046812 (DE-599)BVBBV013791237 |
| dewey-full | 516.3/52 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 516 - Geometry |
| dewey-raw | 516.3/52 |
| dewey-search | 516.3/52 |
| dewey-sort | 3516.3 252 |
| 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>01665nam a2200457 c 4500</leader><controlfield tag="001">BV013791237</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">00000000000000.0</controlfield><controlfield tag="007">t</controlfield><controlfield tag="008">010627s2000 |||| 00||| eng d</controlfield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9810243375</subfield><subfield code="9">981-02-4337-5</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)44046812</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV013791237</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">rakwb</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-20</subfield><subfield code="a">DE-355</subfield><subfield code="a">DE-824</subfield><subfield code="a">DE-11</subfield><subfield code="a">DE-384</subfield></datafield><datafield tag="050" ind1=" " ind2="0"><subfield code="a">QA567.2.E44</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">516.3/52</subfield><subfield code="2">21</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SK 240</subfield><subfield code="0">(DE-625)143226:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Hida, Haruzo</subfield><subfield code="d">1952-</subfield><subfield code="e">Verfasser</subfield><subfield code="0">(DE-588)129238260</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Geometric modular forms and elliptic curves</subfield><subfield code="c">Haruzo Hida</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Singapore [u.a.]</subfield><subfield code="b">World Scientific</subfield><subfield code="c">2000</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">X, 361 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="650" ind1=" " ind2="4"><subfield code="a">Courbes elliptiques</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Curvas eliticas</subfield><subfield code="2">larpcal</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Elliptische oppervlakken</subfield><subfield code="2">gtt</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Formes modulaires</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Geometria algébrica</subfield><subfield code="2">larpcal</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Vormen (wiskunde)</subfield><subfield code="2">gtt</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Curves, Elliptic</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Forms, Modular</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Modulraum</subfield><subfield code="0">(DE-588)4183462-8</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Elliptische Kurve</subfield><subfield code="0">(DE-588)4014487-2</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Elliptische Kurve</subfield><subfield code="0">(DE-588)4014487-2</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2="1"><subfield code="a">Modulraum</subfield><subfield code="0">(DE-588)4183462-8</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="856" ind1="4" ind2="2"><subfield code="m">HBZ Datenaustausch</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=009428378&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA</subfield><subfield code="3">Inhaltsverzeichnis</subfield></datafield><datafield tag="999" ind1=" " ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-009428378</subfield></datafield></record></collection> |
| id | DE-604.BV013791237 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T18:52:02Z |
| institution | BVB |
| isbn | 9810243375 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-009428378 |
| oclc_num | 44046812 |
| open_access_boolean | |
| owner | DE-20 DE-355 DE-BY-UBR DE-824 DE-11 DE-384 |
| owner_facet | DE-20 DE-355 DE-BY-UBR DE-824 DE-11 DE-384 |
| physical | X, 361 S. |
| publishDate | 2000 |
| publishDateSearch | 2000 |
| publishDateSort | 2000 |
| publisher | World Scientific |
| record_format | marc |
| spelling | Hida, Haruzo 1952- Verfasser (DE-588)129238260 aut Geometric modular forms and elliptic curves Haruzo Hida Singapore [u.a.] World Scientific 2000 X, 361 S. txt rdacontent n rdamedia nc rdacarrier Courbes elliptiques Curvas eliticas larpcal Elliptische oppervlakken gtt Formes modulaires Geometria algébrica larpcal Vormen (wiskunde) gtt Curves, Elliptic Forms, Modular Modulraum (DE-588)4183462-8 gnd rswk-swf Elliptische Kurve (DE-588)4014487-2 gnd rswk-swf Elliptische Kurve (DE-588)4014487-2 s Modulraum (DE-588)4183462-8 s DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009428378&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Hida, Haruzo 1952- Geometric modular forms and elliptic curves Courbes elliptiques Curvas eliticas larpcal Elliptische oppervlakken gtt Formes modulaires Geometria algébrica larpcal Vormen (wiskunde) gtt Curves, Elliptic Forms, Modular Modulraum (DE-588)4183462-8 gnd Elliptische Kurve (DE-588)4014487-2 gnd |
| subject_GND | (DE-588)4183462-8 (DE-588)4014487-2 |
| title | Geometric modular forms and elliptic curves |
| title_auth | Geometric modular forms and elliptic curves |
| title_exact_search | Geometric modular forms and elliptic curves |
| title_full | Geometric modular forms and elliptic curves Haruzo Hida |
| title_fullStr | Geometric modular forms and elliptic curves Haruzo Hida |
| title_full_unstemmed | Geometric modular forms and elliptic curves Haruzo Hida |
| title_short | Geometric modular forms and elliptic curves |
| title_sort | geometric modular forms and elliptic curves |
| topic | Courbes elliptiques Curvas eliticas larpcal Elliptische oppervlakken gtt Formes modulaires Geometria algébrica larpcal Vormen (wiskunde) gtt Curves, Elliptic Forms, Modular Modulraum (DE-588)4183462-8 gnd Elliptische Kurve (DE-588)4014487-2 gnd |
| topic_facet | Courbes elliptiques Curvas eliticas Elliptische oppervlakken Formes modulaires Geometria algébrica Vormen (wiskunde) Curves, Elliptic Forms, Modular Modulraum Elliptische Kurve |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009428378&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT hidaharuzo geometricmodularformsandellipticcurves |