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出版社： OUP Oxford
ISBN：9780198502845
商品编码：1098538298
包装：精装
外文名称：Algebraic Geometry and...
出版时间：2002-05-09
页数：592
正文语种：英语
具体描述
图书基本信息
Algebraic Geometry and Arithmetic Curves
作者： Qing Liu;
ISBN13： 9780198502845
类型： 精装(精装书)
语种： 英语（English）
出版日期： 2002-05-09
出版社： OUP Oxford
页数： 592
重量（克）： 1006
尺寸： 23.3934 x 15.5956 x 3.3274 cm
商品简介
This book is a general introduction to 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 theory. The first part ends with the theorem of Riemann-Roch and its application to the study of smooth projective curves over a field. Singular curves are treated through a detailed study of the Picard group. The second part starts with blowing-ups and desingularization (embedded or not) of fibered surfaces over a Dedekind ring that leads on to intersection theory on arithmetic surfaces. Castelnuovo's criterion is proved and also the existence of the minimal regular model. This leads to the study of reduction of algebraic curves. The case of elliptic curves is studied in detail. The book concludes with the fundamental theorem of stable reduction of Deligne-Mumford. The book is essentially self-contained, including the necessary material on commutative algebra. The prerequisites are therefore few, and the book should suit a graduate student. It contains many examples and nearly 600 exercises.用户评价
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