On the fundamental class of an essentially smooth scheme-map

Joseph Lipman, Amnon Neeman

    Research output: Contribution to journalArticlepeer-review

    1 Citation (Scopus)

    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 languageEnglish
    Pages (from-to)131-159
    Number of pages29
    JournalAlgebraic Geometry
    Volume5
    Issue number2
    DOIs
    Publication statusPublished - 1 Mar 2018

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