代数几何

出版时间：2006-11  出版社：清华大学  作者：扶磊  页数：263  
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内容概要

In spirit, this book is closer to Elements de Geometrie Algebrique (EGA) than the existing textbooks on algebraic geometry. It prvides an introduction to schemes, formal schemesc coherent sheaves, and their cohomologies. The prerequisites for reading this book is the knowledge of commutative algebra up to the level of Ateyah-Macdonald's book. The material on algebraic geometry covered in this book provides adequate preparation for reading more advanced books such as Seminaire de Geometrie Algebrique （SGA）.

作者简介

Dr. Lei Fu was born in 1970. He obtained his Bachelor degree from Wuhan University in 1989, and Ph. D. from Rice university （USA）in 1995. He has been a professor of the Chern Institute of Mathematics at nankai university since 1999. His main interest is algebraic geometry and number theory, especially l-adic cohomology theory and its application to the study of varieties over finite fields and local fields.

书籍目录

1  Schemes and Coherent Sheaves	　1.1  Presheaves and Sheaves	　1.2  Schemes and Morphisms	　1.3  Properties of Schemes and Morphisms	　1.4  Coherent Sheaves	　1.5  Formal Completions of Schemes and Sheaves2  Cohomology	　2.1  Derived Functors	　2.2  Spectral Sequences	　2.3  Cech Cohomology	　2.4  Cohomology of Affine and Projective Schemes	　2.5  Cohomological Study of Proper Morphisms	　2.6  Local Freeness of Higher Direct Images	　　2.7  Grothendieck's Existence Theorem		　　Bibliography	Index

用户评论 (总计4条)

•   听扶磊的课，是一种享受，时间常常不知不觉的过去。他讲代数几何就是用得这本书，很不错，值得购买。
•   好书 英文 看着有些费劲
•   还没有仔细读，看样不错，呵呵。
•   不知道天才少年扶磊教授的中文程度如何，想来不会太好，不然这本书怎么不用中文写作。如果这本书用中文写作的话，中国的学生就有福了。不过，即使使用英文写作，也好，毕竟能读懂代数几何的学生，英文程度想来也不会差到哪里去。代数几何教材比较受推崇的是Hartshorne的AlgebraicGeometry，我曾经在当当网上评论说这本书应该每个人手里有一本，即使不看也要有。那是案头书！代数几何还有一本“圣经”，那就是法国农民Grothendieck所写的EGA和SGA。扶磊教授写的这本书也可以说是简写本的“圣经”。我的一位朋友说他正在读代数几何，我问他用什么教材，他说是扶磊教授的这本书。那我就奇怪了，Hartshorne的书不是更好吗，内容丰富，习题量大。他说扶磊的书语言跟现代一些。我觉得扶磊的这本书对于有志于在代数几何方面做出一些成就的朋友来说还是很有帮助的。但是最好同时辅以Hartshorne的书中的习题，这样玩起来才有意思。最后我觉得学习代数几何以前最好把微分几何看看，有用。