Oxford University Press Oxford Algebraic Geometry and Arithmetic Curves Textbook

Expand your mathematical knowledge with this comprehensive guide to algebraic and arithmetic geometry from Oxford University Press. This new paperback edition serves as a foundational resource for students and researchers, offering a structured introduction to the theory of schemes and their diverse applications. Starting with fundamental concepts, the text covers essential topics such as morphisms, base change, and local properties, including normality, regularity, and Zariski's Main Theorem. Readers will progress from these basic objects to more global aspects, such as coherent sheaves and finiteness theorems for cohomology groups. The material also explores sheaves of differentials, dualizing sheaves, and Grothendieck's duality theory. By bridging the gap between scheme theory and arithmetic surfaces, this book provides the necessary tools to understand the reduction of algebraic curves. It is an essential addition to any advanced mathematics library, specifically designed for those studying the Oxford Graduate Texts in Mathematics series.