専門書読書案内
数学を専攻する学部3, 4年, 大学院生向け:
かなり偏りがあります.
参考にして戴ければと思います.
挙げた順序に意味はありません.
また, もちろん, 全部読め, という意味ではありません.
可換環論
- M. Atiyah, I. MacDonald: Introduction to Commutative Algebra (Addison-Wesley)
- H. Matsumura: Commutative Ring Theory (Cambridge)
ホモロジー代数
- R. Godement: Topologie Alg\'ebrique et Th\'eotrie de Faisceux (Hermann)
- 河田敬義: ホモロジー代数 (岩波書店)
代数幾何学: 一般
- W. Fulton: Algebrac Curves (Benjamin)
- D. Cox, J. Little, D. O'Shea: Ideals, Varieties, and Algorithms (Springer)
- D. Mumford: Algebraic Geomety I; Complex Projective Varieties (Springer)
- R. Hartshorne: Algebraic Geometry (GTM52, Springer)
- J. Harris: Algebraic Geometry (GTM133, Springer)
- P. Griffiths, J. Harris: Principles of Algebraic Geometry (Wiley-Interscience)
- D. Mumford: Lectures on Curves on an Algebraic Surfaces (Princeton)
- D. Mumford: The Red Book (Springer)
代数幾何学: トピックス
- C. Okonek, M. Schneider, H. Spindler: Vector Bundles on Complex Projective Spaces (Birkh\"auser)
- D. Mumford: Abelian Varities (Oxford)
- T. Fujita: Classification Theories of Polarized Varieties (LMS)
- D. Mumford: Geometric Invariant Theory (Springer)
- J. Milne: \'Etale Cohomology (Princeton)
- W. Fulton: Intersection Theory (Springer)
- F. Zak: Tangents and Secants of Algebraic Varities (AMS)
- R. Lazarsfeld, A. Van de Ven: Topics in the Geometry of Projective Spaces (Birkh\"auser)
その他, 面白い本
- W. Fulton, J. Harris: Representation Theory (GTM129, Springer)
- D. Collingwood, W. McGovern: Nilpotent Orbits in Semi-simple Lie Algebras (Van Nostrand Reinhold)
- R. Baston, M. Eastwood: The Penrose Transform (Oxford)
- J. Humphreys: Introduction to Lie Algebras and Representation Theoty (GTM9, Springer)
- J. Humphreys: Linear Algebraic Groups (GTM21, Springer)
- D. Cox, J. Little, D. O'Shea: Using Algebraic Goemety (GTM185, Springer)
- I. Satake: Algebraic Structures of Symmetric Domains (Iwanami)
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