GENERALIZED VERDIER DUALITY FOR PRESHEAVES OF SPECTRA .1.

[摘要] The stable homotopy category, with spectra as objects, resembles in many aspects the derived category whose objects are complexes of abelian groups. In this paper, we show that many of the familiar techniques of homological algebra available on the category of presheaves of abelian group spectra can be carried over (with suitable modifications) to the category of presheaves of spectra. Using A infinity-ring spectra, we show that the duality theory of Verdier for abelian presheaves may be generalised to a general duality (called generalised Verdier duality) for presheaves of spectra. Other common duality results, for example duality in the sense of Spanier-Whitehead or Poincare-duality for spectra are interpreted in terms of generalised Verdier duality. One of the goals is to set up a broad framework for defining a presheaf theoretic version of generalised intersection cohomology. The remaining aspects of the theory will be dealt with elsewhere.

[发布日期] 1991-03-29