Algebraic Geometry and Arithmetic Curves

• Includes essential background methods
• Contains nearly 600 exercises to help students assimilate the information and test themselves
• Explains both theory and applications clearly
• Makes important current research accessible to graduate students

Readership: Graduate students in algebraic geometry and number theory

Qing Liu, Chargé de recherche, Centre National de la Recherche Scientifique (CNRS), Laboratoire de Théorie des Nombres et d'Algorithmique Arithmétique, Université Bordeaux 1

"Will be useful to graduate students as an introduction to arithmetic algebraic geometry, and to more advanced readers and experts in the field." - EMS

"This book is unique in the current literature on algebraic and arithmetic geometry, therefore a highly welcome addition to it, and particularly suitable for readers who want to approach more specialized works in this field with more ease. The exposition is exceptionally lucid, rigorous, coherent and comprehensive." - Zentralblatt MATH

"A thorough and far-reaching introduction to algebraic geometry in its scheme-theoretic setting ... The rich bibliography with nearly 100 references enhances the value of this textbook as a great introduction and source for research." - Zentralblatt MATH

Introduction
1: Some topics in commutative algebra
2: General Properties of schemes
3: Morphisms and base change
4: Some local properties
5: Coherent sheaves and Cech cohmology
6: Sheaves of differentials
7: Divisors and applications to curves
8: Birational geometry of surfaces
9: Regular surfaces
10: Reduction of algebraic curves
Bibilography
Index