Duality for Cousin Complexes
| dc.creator | Sastry, Pramathanath | |
| dc.date | 2004-01-15 | |
| dc.date | 2004-06-25 | |
| dc.date.accessioned | 2026-07-07T05:04:33Z | |
| dc.date.available | 2026-07-07T05:04:33Z | |
| dc.description | We relate the variance theory for Cousin complexes -^# developed by Lipman, Nayak and the author to Grothendieck duality for Cousin complexes. Specifically for a Cousin complex F on (Y, Δ)--with Δa codimension function on a formal scheme Y (noetherian, universally catenary)--and a pseudo-finite type map f:(X,Δ') --> (Y,Δ) of such pairs of schemes with codimension functions, we show there is a derived category map γ^!_f(F):f^#F --> f^!F, which is functorial as F varies over Cousin complexes on (Y,Δ), and induces an isomorphism f^#F = E(f^#F) --> E(f^!F). E here is the Cousin functor for the codimension function Δ. Further, we give conditions under which γ^!_f is an isomorphism. We also generalize the Residue Theorem of Grothendieck for residual complexes to Cousin complexes by defining trace as a sum of local residues when the map f is pseudo-proper. | |
| dc.description | 56 pages; minor corrections incorporating referee's comments | |
| dc.identifier | https://arxiv.org/abs/math/0401166 | |
| dc.identifier | http://arxiv.org/abs/math/0401166 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/69848 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | Commutative Algebra | |
| dc.subject | 14B15; 14F99; 1399 | |
| dc.title | Duality for Cousin Complexes | |
| dc.type | text |