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Algebraic G-theory in motivic homotopy categories

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arxiv 1806.03927 v3 pith:LDLDJGAZ submitted 2018-06-11 math.AG math.KT

Fangzhou Jin This is my paper · ORCID
classification math.AGmath.KT
keywords algebraiccategoriesg-theoryhomotopymotivicstableassociatedborel-moore
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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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  1. Duality for KGL-modules in motivic homotopy theory

    math.KT 2025-07 unverdicted novelty 5.0 of 10

    Duality for KH-theory modules in motivic homotopy theory is proven over all quasi-excellent characteristic zero schemes, with G-theory as dualizing object.

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