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 -