On the fundamental class of an essentially smooth scheme-map

Abstract

Let f: X -> Z be a separated essentially-finite-type flat map of noetherian schemes, and δ: X --> X \times_Z X the diagonal map. The fundamental class C_f (globalizing residues) is a map from the relative Hochschild functor Lδ^*δ_* f^* to the relative dualizing functor f^! A compatibility between this C_f and derived tensor product is shown. The main result is that, in a suitable sense, C_f generalizes Verdier's classical isomorphism for smooth f with fibers of dimension d, an isomorphism that binds f^! to relative d-forms.

Minor corrections. 31 pages. To appear in Algebraic Geometry

References in corpus (1)

• An improvement on the base-change theorem and the functor $f^{!}$

Cited by in corpus (2)

• Grothendieck Duality and Transitivity II: Traces and Residues via Verdier's isomorphism
• Grothendieck Duality and Transitivity I: Formal Schemes