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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, Chennai, India
Pramathanath Sastry University of Toronto, Toronto, ON, Canada
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Softcover ISBN: 978-0-8218-3705-4
Product Code: CONM/375
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AMS Member Price: $117.60 Click above image for expanded view Variance and Duality for Cousin Complexes on Formal Schemes Joseph Lipman Purdue University, West Lafayette, IN Suresh Nayak Chennai Mathematical Institute, Chennai, India Pramathanath Sastry University of Toronto, Toronto, ON, Canada Available Formats:  Softcover ISBN: 978-0-8218-3705-4 Product Code: CONM/375  List Price:$98.00 MAA Member Price: $88.20 AMS Member Price:$78.40
 Electronic ISBN: 978-0-8218-7965-8 Product Code: CONM/375.E
 List Price: $92.00 MAA Member Price:$82.80 AMS Member Price: $73.60 Bundle Print and Electronic Formats and Save! This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version.  List Price:$147.00 MAA Member Price: $132.30 AMS Member Price:$117.60
• Book Details

Contemporary Mathematics
Volume: 3752005; 276 pp
MSC: Primary 14; Secondary 18; 32;

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.

• Articles
• Joseph Lipman, Suresh Nayak and Pramathanath Sastry - Pseudofunctorial behavior of Cousin complexes on formal schemes [ MR 2136143 ]
• Pramathanath Sastry - Duality for Cousin complexes [ MR 2136144 ]
• Suresh Nayak - Pasting pseudofunctors [ MR 2136145 ]
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Volume: 3752005; 276 pp
MSC: Primary 14; Secondary 18; 32;

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.