Derived Category Methods in Commutative Algebra

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.

• 1 Modules.- 2 Complexes.- 3 Categorical Constructions.- 4 Equivalences and Isomorphisms.- 5 Resolutions.- 6 The Derived Category.- 7 Derived Functors.- 8 Homological Dimensions.- 9 Gorenstein Homological Dimensions.- 10 Dualizing Complexes.- 11 Torsion and Completion.- 12 A Brief for Commutative Ring Theorists.- 13 Derived Torsion and Completion.- 14 Krull Dimension, Depth, and Width.- 15 Support Theories.- 16 Homological Invariants over Local Rings.- 17 Going Local.- 18 Dualities and Cohen-Macaulay Rings.- 19 Gorenstein Dimensions and Gorenstein Rings.- 20 Global Dimension and Regular Rings.- APPENDIX A: Acyclicity and Boundedness.- APPENDIX B: Minimality.- APPENDIX C: Structure of Injective Modules.- APPENDIX D: Projective Dimension of Flat Modules.- APPENDIX E: Triangulated Categories.