Variance and Duality for Cousin Complexes on Formal Schemes
Robert Hartshorne's book, Residues and Duality (1966, Springer-Verlag), introduced the notion of residual complexes and developed a duality theory (Grothendieck duality) on the category of maps of noetherian schemes. The three articles in this volume constitute a reworking of the main parts of the corresponding chapters in Hartshorne's 1966 book in greater generality using a somewhat different approach. In particular, throughout this volume, the authors work with arbitrary (quasi-coherent, torsion) Cousin complexes on formal schemes, not only with residual complexes on ordinary schemes. Additionally, their motivation is to help readers gain a better understanding of the relation between local properties of residues and global properties of the dualizing pseudofunctor. The book is suitable for graduate students and researchers working in algebraic geometry.
- J. Lipman, S. Nayak, and P. Sastry: Part 1. Pseudofunctorial behavior of Cousin complexes on formal schemes
- P. Sastry: Part 2. Duality for Cousin complexes
- S. Nayak: Part 3. Pasting pseudofunctors