Algebraic geometry and arithmetic curves /:
This new-in-paperback edition provides a general introduction to algebraic and arithmetic geometry, starting with the theory of schemes, followed by applications to arithmetic surfaces and to the theory of reduction of algebraic curves. The first part introduces basic objects such as schemes, morphi...
Gespeichert in:
| 1. Verfasser: | |
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| Weitere Verfasser: | |
| Format: | Elektronisch E-Book |
| Sprache: | English French |
| Veröffentlicht: |
Oxford ; New York :
Oxford University Press,
2006.
|
| Schriftenreihe: | Oxford science publications.
Oxford graduate texts in mathematics ; 6. |
| Schlagworte: | |
| Online-Zugang: | DE-862 DE-863 |
| Zusammenfassung: | This new-in-paperback edition provides a general introduction to algebraic and arithmetic geometry, starting with the theory of schemes, followed by applications to arithmetic surfaces and to the theory of reduction of algebraic curves. The first part introduces basic objects such as schemes, morphisms, base change, local properties (normality, regularity, Zariski's Main Theorem). This is followed by the more global aspect: coherent sheaves and a finiteness theorem for their cohomology groups. Then follows a chapter on sheaves of differentials, dualizing sheaves, and Grothendieck's duality th. |
| Beschreibung: | 1 online resource (xv, 577 pages :) |
| Bibliographie: | Includes bibliographical references (pages 557-561) and index. |
| ISBN: | 9780191547805 0191547808 9781281341396 1281341398 |
Internformat
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| 490 | 1 | |a Oxford graduate texts in mathematics ; |v 6 | |
| 520 | |a This new-in-paperback edition provides a general introduction to algebraic and arithmetic geometry, starting with the theory of schemes, followed by applications to arithmetic surfaces and to the theory of reduction of algebraic curves. The first part introduces basic objects such as schemes, morphisms, base change, local properties (normality, regularity, Zariski's Main Theorem). This is followed by the more global aspect: coherent sheaves and a finiteness theorem for their cohomology groups. Then follows a chapter on sheaves of differentials, dualizing sheaves, and Grothendieck's duality th. | ||
| 504 | |a Includes bibliographical references (pages 557-561) and index. | ||
| 505 | 0 | |a 1 Some topics in commutative algebra; 2 General properties of schemes; 3 Morphisms and base change; 4 Some local properties; 5 Coherent sheaves and Cech cohomology; 6 Sheaves of differentials; 7 Divisors and applications to curves; 8 Birational geometry of surfaces; 9 Regular surfaces; 10 Reduction of algebraic curves; Bibliography; Index. | |
| 546 | |a English. | ||
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| author | Liu, Qing, 1963- |
| author2 | Erné, Reinie |
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| contents | 1 Some topics in commutative algebra; 2 General properties of schemes; 3 Morphisms and base change; 4 Some local properties; 5 Coherent sheaves and Cech cohomology; 6 Sheaves of differentials; 7 Divisors and applications to curves; 8 Birational geometry of surfaces; 9 Regular surfaces; 10 Reduction of algebraic curves; Bibliography; Index. |
| ctrlnum | (OCoLC)646747871 |
| dewey-full | 516.35 |
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| dewey-ones | 516 - Geometry |
| dewey-raw | 516.35 |
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| discipline | Mathematik |
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| id | ZDB-4-EBA-ocn646747871 |
| illustrated | Illustrated |
| indexdate | 2025-03-18T14:15:09Z |
| institution | BVB |
| isbn | 9780191547805 0191547808 9781281341396 1281341398 |
| language | English French |
| oclc_num | 646747871 |
| open_access_boolean | |
| owner | MAIN DE-862 DE-BY-FWS DE-863 DE-BY-FWS |
| owner_facet | MAIN DE-862 DE-BY-FWS DE-863 DE-BY-FWS |
| physical | 1 online resource (xv, 577 pages :) |
| psigel | ZDB-4-EBA FWS_PDA_EBA ZDB-4-EBA |
| publishDate | 2006 |
| publishDateSearch | 2006 |
| publishDateSort | 2006 |
| publisher | Oxford University Press, |
| record_format | marc |
| series | Oxford science publications. Oxford graduate texts in mathematics ; |
| series2 | Oxford science publications Oxford graduate texts in mathematics ; |
| spelling | Liu, Qing, 1963- author https://id.oclc.org/worldcat/entity/E39PCjrFxptGgrkty4JKvwFmHP http://id.loc.gov/authorities/names/no2007005301 Algebraic geometry and arithmetic curves / Qing Liu ; translated by Reinie Erné. Oxford ; New York : Oxford University Press, 2006. 1 online resource (xv, 577 pages :) text txt rdacontent computer c rdamedia online resource cr rdacarrier Oxford science publications Oxford graduate texts in mathematics ; 6 This new-in-paperback edition provides a general introduction to algebraic and arithmetic geometry, starting with the theory of schemes, followed by applications to arithmetic surfaces and to the theory of reduction of algebraic curves. The first part introduces basic objects such as schemes, morphisms, base change, local properties (normality, regularity, Zariski's Main Theorem). This is followed by the more global aspect: coherent sheaves and a finiteness theorem for their cohomology groups. Then follows a chapter on sheaves of differentials, dualizing sheaves, and Grothendieck's duality th. Includes bibliographical references (pages 557-561) and index. 1 Some topics in commutative algebra; 2 General properties of schemes; 3 Morphisms and base change; 4 Some local properties; 5 Coherent sheaves and Cech cohomology; 6 Sheaves of differentials; 7 Divisors and applications to curves; 8 Birational geometry of surfaces; 9 Regular surfaces; 10 Reduction of algebraic curves; Bibliography; Index. English. Print version record. Curves, Algebraic. http://id.loc.gov/authorities/subjects/sh85034916 Arithmetical algebraic geometry. http://id.loc.gov/authorities/subjects/sh87002041 Courbes algébriques. Géométrie algébrique arithmétique. MATHEMATICS Geometry Algebraic. bisacsh Curvas algebraicas embne Arithmetical algebraic geometry fast Curves, Algebraic fast Algebraische Geometrie gnd http://d-nb.info/gnd/4001161-6 Algebraische Kurve gnd http://d-nb.info/gnd/4001165-3 Erné, Reinie, translator. http://id.loc.gov/authorities/names/no2010205355 has work: Algebraic geometry and arithmetic curves (Text) https://id.oclc.org/worldcat/entity/E39PCGjcPtJqGk9VpgmRBcDYvb https://id.oclc.org/worldcat/ontology/hasWork Print version: Liu, Qing, 1963 July- Algebraic geometry and arithmetic curves. Oxford ; New York : Oxford University Press, 2006 0199202494 9780199202492 (OCoLC)65467614 Oxford science publications. http://id.loc.gov/authorities/names/n42027424 Oxford graduate texts in mathematics ; 6. http://id.loc.gov/authorities/names/n96121759 |
| spellingShingle | Liu, Qing, 1963- Algebraic geometry and arithmetic curves / Oxford science publications. Oxford graduate texts in mathematics ; 1 Some topics in commutative algebra; 2 General properties of schemes; 3 Morphisms and base change; 4 Some local properties; 5 Coherent sheaves and Cech cohomology; 6 Sheaves of differentials; 7 Divisors and applications to curves; 8 Birational geometry of surfaces; 9 Regular surfaces; 10 Reduction of algebraic curves; Bibliography; Index. Curves, Algebraic. http://id.loc.gov/authorities/subjects/sh85034916 Arithmetical algebraic geometry. http://id.loc.gov/authorities/subjects/sh87002041 Courbes algébriques. Géométrie algébrique arithmétique. MATHEMATICS Geometry Algebraic. bisacsh Curvas algebraicas embne Arithmetical algebraic geometry fast Curves, Algebraic fast Algebraische Geometrie gnd http://d-nb.info/gnd/4001161-6 Algebraische Kurve gnd http://d-nb.info/gnd/4001165-3 |
| subject_GND | http://id.loc.gov/authorities/subjects/sh85034916 http://id.loc.gov/authorities/subjects/sh87002041 http://d-nb.info/gnd/4001161-6 http://d-nb.info/gnd/4001165-3 |
| title | Algebraic geometry and arithmetic curves / |
| title_auth | Algebraic geometry and arithmetic curves / |
| title_exact_search | Algebraic geometry and arithmetic curves / |
| title_full | Algebraic geometry and arithmetic curves / Qing Liu ; translated by Reinie Erné. |
| title_fullStr | Algebraic geometry and arithmetic curves / Qing Liu ; translated by Reinie Erné. |
| title_full_unstemmed | Algebraic geometry and arithmetic curves / Qing Liu ; translated by Reinie Erné. |
| title_short | Algebraic geometry and arithmetic curves / |
| title_sort | algebraic geometry and arithmetic curves |
| topic | Curves, Algebraic. http://id.loc.gov/authorities/subjects/sh85034916 Arithmetical algebraic geometry. http://id.loc.gov/authorities/subjects/sh87002041 Courbes algébriques. Géométrie algébrique arithmétique. MATHEMATICS Geometry Algebraic. bisacsh Curvas algebraicas embne Arithmetical algebraic geometry fast Curves, Algebraic fast Algebraische Geometrie gnd http://d-nb.info/gnd/4001161-6 Algebraische Kurve gnd http://d-nb.info/gnd/4001165-3 |
| topic_facet | Curves, Algebraic. Arithmetical algebraic geometry. Courbes algébriques. Géométrie algébrique arithmétique. MATHEMATICS Geometry Algebraic. Curvas algebraicas Arithmetical algebraic geometry Curves, Algebraic Algebraische Geometrie Algebraische Kurve |
| work_keys_str_mv | AT liuqing algebraicgeometryandarithmeticcurves AT ernereinie algebraicgeometryandarithmeticcurves |