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arXiv · 1501.00954

On the fundamental class of an essentially smooth scheme-map

Joseph Lipman·Amnon Neeman
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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.

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Joseph Lipman, Amnon Neeman. 2017-01-14. On the fundamental class of an essentially smooth scheme-map. https://doi.org/10.14231/ag-2018-005

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