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

By:

Liu, Qing, 1963-

Material type: Text

TextLanguage: English Original language: French Series: Oxford science publications | Oxford graduate texts in mathematics ; 6.Publication details: Oxford ; New York : Oxford University Press, 2006.Description: 1 online resource (xv, 577 pages) : illustrationsContent type:

text

Media type:

computer

Carrier type:

online resource

ISBN:

9780191547805
0191547808
0198502842
9780198502845
1281341398
9781281341396
0199202494
9780199202492

Subject(s):

Genre/Form:

Additional physical formats: Print version:: Algebraic geometry and arithmetic curves.DDC classification:

516.35 22

LOC classification:

QA565 .L68 2006eb

Online resources:

Click here to access online

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.

Summary: 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.

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Includes bibliographical references (pages 557-561) and index.

Print version record.

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.

English.

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