Algebraic geometry and arithmetic curves / Qing Liu ; translated by Reinie Erné.

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...

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Bibliographic Details
Main Author: Liu, Qing, 1963- (Author)
Other Authors: Erné, Reinie (Translator)
Format: eBook
Language:English
French
Published: Oxford ; New York : Oxford University Press, 2006.
Series:Oxford science publications.
Oxford graduate texts in mathematics ; 6.
Subjects:
Online Access:Click for online access

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245 1 0 |a Algebraic geometry and arithmetic curves /  |c Qing Liu ; translated by Reinie Erné. 
260 |a Oxford ;  |a New York :  |b Oxford University Press,  |c 2006. 
300 |a 1 online resource (xv, 577 pages) :  |b illustrations. 
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490 1 |a Oxford science publications 
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. 
588 0 |a Print version record. 
650 0 |a Curves, Algebraic. 
650 0 |a Arithmetical algebraic geometry. 
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650 7 |a Curvas algebraicas  |2 embne 
650 7 |a Arithmetical algebraic geometry  |2 fast 
650 7 |a Curves, Algebraic  |2 fast 
650 7 |a Algebraische Geometrie  |2 gnd 
650 7 |a Algebraische Kurve  |2 gnd 
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700 1 |a Erné, Reinie,  |e translator.  |1 https://id.oclc.org/worldcat/entity/E39PCjvvTjWChr7bgHHfPThBmq 
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830 0 |a Oxford science publications. 
830 0 |a Oxford graduate texts in mathematics ;  |v 6. 
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