An l-adic norm residue epimorphism theorem

2024/09/16 by Bruno Kahn, Kahn, Bruno
Mathematics · #11G25 #14C35 #19E15 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometric and Algebraic Topology #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2409.10248

openalex publication_date 2024/09/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/02

Abstract

We show that the continuous étale cohomology groups Hⁿ_cont(X,Z_l(n)) of smooth varieties X over a finite field k are spanned as Z_l-modules by the n-th Milnor K-sheaf locally for the Zariski topology, for all n≥ 0. Here l is a prime invertible in k. This is the first general unconditional result towards the conjectures of arXiv:math/9801017 (math.AG) which put together the Tate and the Beilinson conjectures relative to algebraic cycles on smooth projective k-varieties.

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