Coherent Functors

✍ Scribed by Robin Hartshorne

• Book ID: 102966954
• Publisher: Elsevier Science
• Year: 1998
• Tongue: English
• Weight: 580 KB
• Volume: 140
• Category: Article
• ISSN: 0001-8708
• DOI: 10.1006/aima.1998.1762

✦ Synopsis

We develop Auslander's theory of coherent functors in the case of functors on modules of finite type over a noetherian ring A. In particular, the duality of coherent functors, which interchanges representable functors and tensor products, plays a special role. We apply these coherent functors to study cohomology of a flat family of sheaves on projective space over an affine base scheme T=Spec A. These results form a basic tool which is used in forthcoming work on the variation of the Rao module in a flat family of curves in P 3 .