Derived algebraic geometry is a far-reaching generalization of algebraic geometry. It has found numerous applications in various parts of mathematics, most prom

The first systematic exposition of the theory of derived categories, with key applications in commutative and noncommutative algebra.

This work is based on a course given at the Institut de Mathematiques de Jussieu, on the derived category of coherent sheaves on a smooth projective variety. It

The study of derived categories is a subject that attracts increasingly many mathematicians from various fields of mathematics, including abstract algebra, alge

An array of general ideas useful in a wide variety of fields. Starting from the foundations, this book illuminates the concepts of category, functor, natural tr