Effective Grothendieck-Witt motives of smooth varieties

2017/09/19 by Andrei Druzhinin, Druzhinin, Andrei · 1 citation
Mathematics · #14F42 #19E20 #19G12 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #K-Theory and Homology (math.KT)

paper · pdf · doi:10.48550/arxiv.1709.06273

openalex publication_date 2017/09/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The category of effective Grothendieck-Witt-motives DM^GW_eff,-(k) (and Witt-motives DM^W_eff,-(k)) by Voevodsky-Suslin method starting with some category of GW-correspondences (and Witt-correspondences) over a perfect field k, char k≠ 2, is defined. The functor M^GW_eff\colon Sm_k→ DM^GW_eff,-(k) of Grothendieck-Witt-motives of smooth varieties is computed and it is proved that for any smooth scheme X and homotopy invariant sheave with GW-transfers F Hom_DM^GW_eff,-(k)(M^GW_eff(X), F[i]) ≃ Hⁱ_nis(X, F) naturally in X and F.

Citations

• Finite Chow-Witt correspondences
• Strictly homotopy invariance of Nisnevich sheaves with GW-transfers

Cited by

• On the effectivity of spectra representing motivic cohomology theories

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• Triangulated category of effective Witt-motives DWM^-_eff(k)
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• Strictly homotopy invariance of Nisnevich sheaves with GW-transfers
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