Abstract
Let f: X → Z be a separated, essentially finite-type, flat map of noetherian schemes and δ: X → X×ZX the diagonal map. The fundamental class Cf (globalizing residues) is a map from the relative Hochschild functor Lδ*δ*f* to the relative dualizing functor f!. We show a compatibility between Cf and the derived tensor product. The main result is that, in a suitable sense, Cf generalizes Verdier's classical isomorphism for smooth f with fibers of dimension d, an isomorphism that binds f! to relative d-forms.
Original language | English |
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Pages (from-to) | 131-159 |
Number of pages | 29 |
Journal | Algebraic Geometry |
Volume | 5 |
Issue number | 2 |
DOIs | |
Publication status | Published - 1 Mar 2018 |