Duality and flat base change on formal schemes

Details Duality and flat base change on formal schemes Duality and flat base change on formal schemes

1997-08-04

arxiv.org/abs/alg-geom/9708006v3

Contemporary Math. 244 (1999), 3-90

Mathematics

Commutative Algebra

89 pages. Change from published version: in section 2.5, about dualizing complexes on formal schemes, a weakening of one flawe

Scientific paper

We give several related versions of global Grothendieck Duality for unbounded complexes on noetherian formal schemes. The proofs, based on a non-trivial adaptation of Deligne's method for the special case of ordinary schemes, are reasonably self-contained, modulo the Special Adjoint Functor Theorem. An alternative approach, inspired by Neeman and based on recent results about "Brown Representability," is indicated as well. A section on applications and examples illustrates how these theorems synthesize a number of different duality-related results (local duality, formal duality, residue theorems, dualizing complexes...). A flat-base-change theorem for pseudo-proper maps leads in particular to sheafified versions of duality for bounded-below complexes with quasi-coherent homology. Thanks to Greenlees-May duality, the results take a specially nice form for proper maps and bounded-below complexes with coherent homology.

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