TY - JOUR
T1 - Traces and residues
AU - Neeman, Amnon
N1 - Publisher Copyright:
© Indiana University Mathematics Journal.
PY - 2015
Y1 - 2015
N2 - Let f : X → Y be a separated morphism of Noetherian schemes, and let W ⊂ X be a union of closed subsets such that the restriction of f to each of them is proper. In duality theory, one considers trace maps Rf∗R⌈wf! !OY → OY. In a recent paper, we gave a new construction of such a trace map, using a certain natural transformation ψ(f) : fx -→ f!. In this note, we show how to compute it. In duality theory, there are abstract, functorial definitions, and there are computationally useful formulas, but they are rarely the same. This makes the new approach remarkable.
AB - Let f : X → Y be a separated morphism of Noetherian schemes, and let W ⊂ X be a union of closed subsets such that the restriction of f to each of them is proper. In duality theory, one considers trace maps Rf∗R⌈wf! !OY → OY. In a recent paper, we gave a new construction of such a trace map, using a certain natural transformation ψ(f) : fx -→ f!. In this note, we show how to compute it. In duality theory, there are abstract, functorial definitions, and there are computationally useful formulas, but they are rarely the same. This makes the new approach remarkable.
KW - Derived categories
KW - Grothendieck duality
UR - http://www.scopus.com/inward/record.url?scp=84923784546&partnerID=8YFLogxK
U2 - 10.1512/iumj.2015.64.5461
DO - 10.1512/iumj.2015.64.5461
M3 - Article
SN - 0022-2518
VL - 64
SP - 217
EP - 229
JO - Indiana University Mathematics Journal
JF - Indiana University Mathematics Journal
IS - 1
ER -