Duality for KH-theory modules in motivic homotopy theory is proven over all quasi-excellent characteristic zero schemes, with G-theory as dualizing object.
Algebraic G-theory in motivic homotopy categories
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abstract
We prove that algebraic G-theory in is representable in unstable and stable motivic homotopy categories; in the stable category we identify it with the Borel-Moore theory associated to algebraic K-theory, and show that such an identification is compatible with the functorialities defined by Quillen and Thomason.
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Duality for KGL-modules in motivic homotopy theory
Duality for KH-theory modules in motivic homotopy theory is proven over all quasi-excellent characteristic zero schemes, with G-theory as dualizing object.