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Variance and Duality for Cousin Complexes on Formal Schemes
Joseph Lipman, Purdue University, West Lafayette, IN, Suresh Nayak, Chennai Mathematical Institute, India, and Pramathanath Sastry, University of Toronto, ON, Canada
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Contemporary Mathematics
2005; 276 pp; softcover
Volume: 375
ISBN-10: 0-8218-3705-2
ISBN-13: 978-0-8218-3705-4
List Price: US$87 Member Price: US$69.60
Order Code: CONM/375

Robin Hartshorne's classical 1966 book "Residues and Duality" [RD] developed Alexandre Grothendieck's ideas for a pseudofunctorial variance theory of residual complexes and duality for maps of noetherian schemes.

The three articles in this volume rework the main parts of the last two chapters in [RD], in greater generality--for Cousin complexes on formal schemes, not just residual complexes on ordinary schemes--and by more concrete local methods which clarify the relation between local properties of residues and global properties of dualizing pseudofunctors. A new approach to pasting pseudofunctors is applied in using residual complexes to construct a dualizing pseudofunctor over a fairly general category of formal schemes, where compactifications of maps may not be available.

A theory of traces and duality with respect to pseudo-proper maps is then developed for Cousin complexes. For composites of compactifiable maps of formal schemes, this, together with the above pasting technique, enables integration of the variance theory for Cousin complexes with the very different approach to duality initiated by Deligne in the appendix to [RD].

The book is suitable for advanced graduate students and researchers in algebraic geometry.

Graduate students and researchers interested 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
• Index