代数几何IV
2009-1
科学出版社
帕尔申
284
无
要使我国的数学事业更好地发展起来，需要数学家淡泊名利并付出更艰苦地努力。另一方面，我们也要从客观上为数学家创造更有利的发展数学事业的外部环境，这主要是加强对数学事业的支持与投资力度，使数学家有较好的工作与生活条件，其中也包括改善与加强数学的出版工作。 从出版方面来讲，除了较好较快地出版我们自己的成果外，引进国外的先进出版物无疑也是十分重要与必不可少的。从数学来说，施普林格（springer）出版社至今仍然是世界上最具权威的出版社。科学出版社影印一批他们出版的好的新书，使我国广大数学家能以较低的价格购买，特别是在边远地区工作的数学家能普遍见到这些书，无疑是对推动我国数学的科研与教学十分有益的事。 这次科学出版社购买了版权，一次影印了23本施普林格出版社出版的数学书，就是一件好事，也是值得继续做下去的事情。大体上分一下，这23本书中，包括基础数学书5本，应用数学书6本与计算数学书12本，其中有些书也具有交叉性质。这些书都是很新的，2000年以后出版的占绝大部分，共计16本，其余的也是1990年以后出版的。这些书可以使读者较快地了解数学某方面的前沿，例如基础数学中的数论、代数与拓扑三本，都是由该领域大数学家编著的“数学百科全书”的分册。对从事这方面研究的数学家了解该领域的前沿与全貌很有帮助。按照学科的特点，基础数学类的书以“经典”为主，应用和计算数学类的书以“前沿”为主。这些书的作者多数是国际知名的大数学家，例如《拓扑学》一书的作者诺维科夫是俄罗斯科学院的院士，曾获“菲尔兹奖”和“沃尔夫数学奖”。这些大数学家的著作无疑将会对我国的科研人员起到非常好的指导作用。 当然，23本书只能涵盖数学的一部分，所以，这项工作还应该继续做下去。更进一步，有些读者面较广的好书还应该翻译成中文出版，使之有更大的读者群。 总之，我对科学出版社影印施普林格出版社的部分数学著作这一举措表示热烈的支持，并盼望这一工作取得更大的成绩。
This book contains two contributions on closely related subjects: the theory of linear algebraic groups and invariant theory. The first part is written by T. A. Springer, a well-known expert in the first mentioned field. Hc presents a comprehensive survey, which contains numerous sketched proofs and he discusses the particular features of algebraic groups over special fields (finite, local, and global). The authors of part two-E. B. Vinbcrg and V. L. Popov-arc among the most active researchers in invariant theory. The last 20 years have bccn a period of vigorous development in this field duc to the influence of modern methods from algebraic geometry. The book will bc very useful as a reference and research guide to graduate students and researchers in mathematics and theoretical physics.
I.Linear algebraic Groups Introduction Historical Comments Chapter 1.Linear Algebraic Groups over an Algebraically 1.Recollections from Algebraic Geometry 1.1.Affine Varieties 1.2.Morphisms 1.3.Some Topological Properties 1.4.Tangent Spaces 1.5.Properties of Morphisms 1.6.Non-Affine Varieties 2.Linear Algebraic Groups, Basic Definitions and Properties 2.1.The Definition of a Linear Algebraic Group 2.2.Some Basic Facts 2.3.G-Spaces 2.4.The Lie Algebra of an Algebraic Group 2.5.Quotients 3.Structural Properties of Linear Algebraic Groups 3.1.Jordan Decomposition and Related Results 3.2.Diagonalizable Groups and Tori 3.3.One-Dimensional Connected Groups 3.4.Connected Solvable Groups 3.5.Parabolic Subgroups and Borel Subgroups 3.6.Radicals, Semi-simple and Reductive Groups 4.Reductive Groups 4.1.Groups of Rank One 4.2.The Root Datum and the Root System 4.3.Basic Properties of Reductive Groups 4.4.Existence and Uniqueness Theorems for Reductive Groups 4.5.Classification of Quasi-simple Linear Algebraic Groups 4.6.Representation Theory Chapter 2.Linear Algebraic Groups over Arbitrary Ground Fields 1.Recollections from Algebraic Geometry 1.1.F-Structures on Affine Varieties 1.2.F-Structures on Arbitrary Varieties 1.3.Forms 1.4.Restriction of the Ground Field 2.F-Groups, Basic Properties 2.1.Generalities About F-Groups 2.2.Quotients 2.3.Forms 2.4.Restriction of the Ground Field 3.Tori 3.1.F-Tori 3.2.F-Tori in F-Groups 3.3.Split Tori in F-Groups 4.Solvable Groups 4.1.Solvable Groups 4.2.Sections 4.3.Elementary Unipotent Groups 4.4.Properties of Split Solvable Groups 4.5.Basic Results About Solvable F-Groups 5.Reductive Groups 5.1.Split Reductive Groups 5.2.Parabolic Subgroups 5.3.The Small Root System 5.4.The Groups G(F) 5.5.The Spherical Tits Building of a Reductive F-Group 6.Classification of Reductive F-Groups 6.1.Isomorphism Theorem 6.2.Existence 6.3.Representation Theory of F-Groups Chapter 3.Special Fields 1.Lie Algebras of Algebraic Groups in Characteristic Zero 1.1.Algebraic Subalgebras 2.Algebraic Groups and Lie Groups 2.1.Locally Compact Fields 2.2.Real Lie Groups 3.Linear Algebraic Groups over Finite Fields 3.1.Lang's Theorem and its Consequences 3.2.Finite Groups of Lie Type 3.3.Representations of Finite Groups of Lie Type 4.Linear Algebraic Groups over Fields with a Valuation 4.1.The Apartment and Affine Dynkin Diagram 4.2.The Affine Building 4.3.Tits System, Decompositions 4.4.Local Fields 5.Global Fields 5.1.Adele Groups 5.2.Reduction Theory 5.3.Finiteness Results 5.4.Galois Cohomology ReferencesII.Invariant TheoryAutbor IndexSubject Index
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代数几何权威参考书，简明扼要
这本书蛮好的，很好的参考书
经典好书，有点难，正在阅读中~
当工具书查阅非常好。