Once again on an analogue of the certain Voevodsky theorem

2025/06/07 by Ivan Panin, Panin, Ivan, Dimitrii Nikolaevich Tyurin +1
Mathematics · #FOS: Mathematics #Geometry and complex manifolds #Holomorphic and Operator Theory #K-Theory and Homology (math.KT) #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.2506.06795

openalex publication_date 2025/06/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Suppose that F is an \mathbbA¹-invariant quasi-stable ℤF_∗-presheaf. Then its Zariski sheafification F_Zar coincides with its Nisnevich sheafification F_Nis. Moreover, if X∈ Sm/k is k-smooth, then for any n there is equality Hⁿ_Zar(X, F_Zar)=Hⁿ_Nis(X,F_Nis).

Citations

• Surjectivity of the etale excision map for homotopy invariant framed presheaves
• Homotopy invariant presheaves with framed transfers
• Framed motives of algebraic varieties (after V. Voevodsky)

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• Nice triples and a moving lemma for motivic spaces
• \mathbbA¹-connected components of classifying spaces and purity for torsors
• Strictly homotopy invariance of Nisnevich sheaves with GW-transfers
• Generalising Bogomolov's Inequality to Unstable Sheaves