Derived category methods entered commutative algebra in the latter half of the 1960s, providing, among other things, a framework for a clear formulation of Grothendieck's Local Duality Theorem. Since then, their impact on the field has steadily grown and continues to expand.

This book guides readers familiar with rings and modules through the construction of the associated derived category and its triangulated functors. In this context, it develops theories of categorical equivalences for subcategories and homological invariants of objects. The second half of the book focuses on applications to commutative Noetherian rings.

The book can be used as a text for graduate courses, both introductory and advanced, and is intended to serve as a reference for researchers in commutative algebra and related fields. To accommodate readers new to homological algebra, it offers a significantly higher level of detail than most existing texts on the subject.

Autorentext

Lars Winther Christensen is since 2016 Professor of Mathematics at Texas Tech University. He received his Ph.D. from the University of Copenhagen in 1999 under the direction of Hans-Bjørn Foxby. He is the author of more than 50 research articles and book chapters and maintains active research programs in commutative algebra and homological algebra of rings. His first book was Gorenstein Dimensions (2000).

Hans-Bjørn Foxby (1947-2014) was appointed Associate Professor of Mathematics at the University of Copenhagen in 1975 and promoted to Docent in 1988. He received his Ph.D. in 1973 from the same institution under the direction of Christian U. Jensen. He published more than 30 highly influential research papers and is known for his contributions to commutative algebra.

Henrik Holm is since 2011 Associate Professor of Mathematics at the University of Copenhagen. He received his Ph.D. in 2004 from the same institution under the direction of Hans-Bjørn Foxby. He has published more than 30 research papers in homological algebra, ring theory, and category theory and is known for his contributions to Gorenstein homological algebra.