Algebraic function fields and codes:
Gespeichert in:
| Weitere Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Berlin ; Heidelberg
Springer
2009
|
| Ausgabe: | second edition |
| Schriftenreihe: | Graduate texts in mathematics
254 |
| Schlagworte: | |
| Online-Zugang: | BTU01 TUM01 UBA01 UBM01 UBT01 UER01 UPA01 Volltext Inhaltsverzeichnis |
| Beschreibung: | 1 Online-Ressource |
| ISBN: | 9783540768784 |
| DOI: | 10.1007/978-3-540-76878-4 |
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Datensatz im Suchindex
| _version_ | 1804139040103989248 |
|---|---|
| adam_text | CONTENTS 1 FOUNDATIONS OF THE THEORY OF ALGEBRAIC FUNCTION FIELDS ... 1
1.1 PLACES 1 1.2 THE RATIONAL FUNCTION FIELD 8 1.3 INDEPENDENCE OF
VALUATIONS 12 1.4 DIVISORS 15 1.5 THE RIEMANN-ROCH THEOREM 24 1.6 SOME
CONSEQUENCES OF THE RIEMANN-ROCH THEOREM 31 1.7 LOCAL COMPONENTS OF WEIL
DIFFERENTIALS 37 1.8 EXERCISES 40 2 ALGEBRAIC GEOMETRY CODES 45 2.1
CODES 45 2.2 AG CODES 48 2.3 RATIONAL AG CODES 55 2.4 EXERCISES 63 3
EXTENSIONS OF ALGEBRAIC FUNCTION FIELDS 67 3.1 ALGEBRAIC EXTENSIONS OF
FUNCTION FIELDS 68 3.2 SUBRINGS OF FUNCTION FIELDS 77 3.3 LOCAL INTEGRAL
BASES 81 3.4 THE COTRACE OF WEIL DIFFERENTIALS AND THE HURWITZ GENUS
FORMULA 90 3.5 THE DIFFERENT 99 3.6 CONSTANT FIELD EXTENSIONS 112 3.7
GALOIS EXTENSIONS I 120 3.8 GALOIS EXTENSIONS II 130 3.9 RAMIFICATION
AND SPLITTING IN THE COMPOSITUM OF FUNCTION FIELDS 137 3.10 INSEPARABLE
EXTENSIONS 143 3.11 ESTIMATES FOR THE GENUS OF A FUNCTION FIELD 145 3.12
EXERCISES 150 BIBLIOGRAFISCHE INFORMATIONEN HTTP://D-NB.INFO/990669424
DIGITALISIERT DURCH XII CONTENTS 4 DIFFERENTIALS OF ALGEBRAIC FUNCTION
FIELDS 155 4.1 DERIVATIONS AND DIFFERENTIALS 155 4.2 THE P-ADIC
COMPLETION 161 4.3 DIFFERENTIALS AND WEIL DIFFERENTIALS 170 4.4
EXERCISES 179 5 ALGEBRAIC FUNCTION FIELDS OVER FINITE CONSTANT FIELDS
185 5.1 THE ZETA FUNCTION OF A FUNCTION FIELD 185 5.2 THE HASSE-WEIL
THEOREM 197 5.3 IMPROVEMENTS OF THE HASSE-WEIL BOUND 208 5.4 EXERCISES
212 6 EXAMPLES OF ALGEBRAIC FUNCTION FIELDS 217 6.1 ELLIPTIC FUNCTION
FIELDS 217 6.2 HYPERELLIPTIC FUNCTION FIELDS 224 6.3 TARNE CYCLIC
EXTENSIONS OF THE RATIONAL FUNCTION FIELD 227 6.4 SOME ELEMENTARY
ABELIAN P-EXTENSIONS OF K(X), CHAXK = P 0 232 6.5 EXERCISES 235 7
ASYMPTOTIC BOUNDS FOR THE NUMBER OF RATIONAL PLACES .... 243 7.1 IHARA S
CONSTANT A{Q) 243 7.2 TOWERS OF FUNCTION FIELDS 246 7.3 SOME TARNE
TOWERS 259 7.4 SOME WILD TOWERS 261 7.5 EXERCISES 285 8 MORE ABOUT
ALGEBRAIC GEOMETRY CODES 289 8.1 THE RESIDUE REPRESENTATION OF C N {D,
G) 289 8.2 AUTOMORPHISMS OF AG CODES 290 8.3 HERMITIAN CODES 292 8.4 THE
TSFASMAN-VLADUT-ZINK THEOREM 297 8. CONTENTS XIII REFERENCES 349 INDEX
353
|
| any_adam_object | 1 |
| author2 | Stichtenoth, Henning 1944- |
| author2_role | edt |
| author2_variant | h s hs |
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| dewey-full | 512.74 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
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| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1007/978-3-540-76878-4 |
| edition | second edition |
| format | Electronic eBook |
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| spelling | Algebraic function fields and codes Henning Stichtenoth second edition Berlin ; Heidelberg Springer 2009 1 Online-Ressource txt rdacontent c rdamedia cr rdacarrier Graduate texts in mathematics 254 Algebraische Funktion (DE-588)4141836-0 gnd rswk-swf Fehlerkorrekturcode (DE-588)4124917-3 gnd rswk-swf Codierungstheorie (DE-588)4139405-7 gnd rswk-swf Algebraischer Funktionenkörper (DE-588)4141850-5 gnd rswk-swf Algebraischer Funktionenkörper (DE-588)4141850-5 s Codierungstheorie (DE-588)4139405-7 s DE-604 Fehlerkorrekturcode (DE-588)4124917-3 s 1\p DE-604 Algebraische Funktion (DE-588)4141836-0 s 2\p DE-604 Stichtenoth, Henning 1944- (DE-588)141456280 edt Erscheint auch als Druck-Ausgabe Graduate texts in mathematics 254 (DE-604)BV035421258 254 https://doi.org/10.1007/978-3-540-76878-4 Verlag URL des Erstveröffentlichers Volltext DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017480634&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Algebraic function fields and codes Graduate texts in mathematics Algebraische Funktion (DE-588)4141836-0 gnd Fehlerkorrekturcode (DE-588)4124917-3 gnd Codierungstheorie (DE-588)4139405-7 gnd Algebraischer Funktionenkörper (DE-588)4141850-5 gnd |
| subject_GND | (DE-588)4141836-0 (DE-588)4124917-3 (DE-588)4139405-7 (DE-588)4141850-5 |
| title | Algebraic function fields and codes |
| title_auth | Algebraic function fields and codes |
| title_exact_search | Algebraic function fields and codes |
| title_full | Algebraic function fields and codes Henning Stichtenoth |
| title_fullStr | Algebraic function fields and codes Henning Stichtenoth |
| title_full_unstemmed | Algebraic function fields and codes Henning Stichtenoth |
| title_short | Algebraic function fields and codes |
| title_sort | algebraic function fields and codes |
| topic | Algebraische Funktion (DE-588)4141836-0 gnd Fehlerkorrekturcode (DE-588)4124917-3 gnd Codierungstheorie (DE-588)4139405-7 gnd Algebraischer Funktionenkörper (DE-588)4141850-5 gnd |
| topic_facet | Algebraische Funktion Fehlerkorrekturcode Codierungstheorie Algebraischer Funktionenkörper |
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