代數幾何

代數幾何

图书基本信息
出版时间:2006-11
出版社:清華大學
作者:扶磊
页数:263
书名:代數幾何
封面图片
代數幾何
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
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评论与打分
  •     听扶磊的課,是一種享受,時間常常不知不覺的過去。他講代數幾何就是用得這本書,很不錯,值得購買。
  •     好書 英文 看著有些費勁
  •     還沒有仔細讀,看樣不錯,呵呵。
  •     不知道天才少年扶磊教授的中文程度如何,想來不會太好,不然這本書怎麼不用中文寫作。如果這本書用中文寫作的話,中國的學生就有福了。不過,即使使用英文寫作,也好,畢竟能讀懂代數幾何的學生,英文程度想來也不會差到哪里去。代數幾何教材比較受推崇的是Hartshorne的AlgebraicGeometry,我曾經在當當網上評論說這本書應該每個人手里有一本,即使不看也要有。那是案頭書!代數幾何還有一本“聖經”,那就是法國農民Grothendieck所寫的EGA和SGA。扶磊教授寫的這本書也可以說是簡寫本的“聖經”。我的一位朋友說他正在讀代數幾何,我問他用什麼教材,他說是扶磊教授的這本書。那我就奇怪了,Hartshorne的書不是更好嗎,內容豐富,習題量大。他說扶磊的書語言跟現代一些。我覺得扶磊的這本書對于有志于在代數幾何方面做出一些成就的朋友來說還是很有幫助的。但是最好同時輔以Hartshorne的書中的習題,這樣玩起來才有意思。最後我覺得學習代數幾何以前最好把微分幾何看看,有用。