Algebraic geometry and arithmetic curves /
Liu, Qing, 1963-
Algebraic geometry and arithmetic curves / Qing Liu ; translated by Reinie Erné. - Oxford ; New York : Oxford University Press, 2006. - 1 online resource (xv, 577 pages) : illustrations - Oxford science publications Oxford graduate texts in mathematics ; 6 . - Oxford science publications. Oxford graduate texts in mathematics ; 6. .
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.
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.
9780191547805 (electronic bk.) 0191547808 (electronic bk.) 0198502842 9780198502845 1281341398 9781281341396 0199202494 9780199202492
Curves, Algebraic.
Arithmetical algebraic geometry.
Courbes algébriques.
Géométrie algébrique arithmétique.
MATHEMATICS--Geometry--Algebraic.
Arithmetical algebraic geometry.
Curves, Algebraic.
Electronic books.
Electronic books.
QA565 / .L68 2006eb
516.35
Algebraic geometry and arithmetic curves / Qing Liu ; translated by Reinie Erné. - Oxford ; New York : Oxford University Press, 2006. - 1 online resource (xv, 577 pages) : illustrations - Oxford science publications Oxford graduate texts in mathematics ; 6 . - Oxford science publications. Oxford graduate texts in mathematics ; 6. .
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.
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.
9780191547805 (electronic bk.) 0191547808 (electronic bk.) 0198502842 9780198502845 1281341398 9781281341396 0199202494 9780199202492
Curves, Algebraic.
Arithmetical algebraic geometry.
Courbes algébriques.
Géométrie algébrique arithmétique.
MATHEMATICS--Geometry--Algebraic.
Arithmetical algebraic geometry.
Curves, Algebraic.
Electronic books.
Electronic books.
QA565 / .L68 2006eb
516.35