Grothendieck duality via homotopy theory

Details Grothendieck duality via homotopy theory Grothendieck duality via homotopy theory

1994-12-27

arxiv.org/abs/alg-geom/9412022v1

Mathematics

Algebraic Geometry

31 pages, AMS-LaTeX. To appear in Jour. AMS.

Scientific paper

Grothendieck proved that if $f:X\longrightarrow Y$ is a proper morphism of nice schemes, then $Rf_*$ has a right adjoint, which is given as tensor product with the relative canonical bundle. The original proof was by patching local data. Deligne proved the existence of the adjoint by a global argument, and Verdier showed that this global adjoint may be computed locally. In this article we show that the existence of the adjoint is an immediate consequence of Brown's representability theorem. It follows almost as immediately, by ``smashing'' arguments, that the adjoint is given by tensor product with a dualising complex. Verdier's base change theorem is an immediate consequence.

Affiliated with

Also associated with

No associations

Rating

Grothendieck duality via homotopy theory does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Grothendieck duality via homotopy theory, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Grothendieck duality via homotopy theory will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-178178