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）.
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.
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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