On the fundamental class of an essentially smooth scheme-map
Copyright policy )On the fundamental class of an essentially smooth scheme-map
Let f: X -> Z be a separated essentially-finite-type flat map of noetherian schemes, and ��: X --> X \times_Z X the diagonal map. The fundamental class C_f (globalizing residues) is a map from the relative Hochschild functor L��^*��_* 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
- Mathematical Sciences Research Institute United States
Mathematics - Algebraic Geometry, FOS: Mathematics, 14F05, 14F10, 13D03, Mathematics - Commutative Algebra, Commutative Algebra (math.AC), Algebraic Geometry (math.AG)
Mathematics - Algebraic Geometry, FOS: Mathematics, 14F05, 14F10, 13D03, Mathematics - Commutative Algebra, Commutative Algebra (math.AC), Algebraic Geometry (math.AG)
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