Remarks on Milnor K-theory and Tate's conjecture for divisors

2024/06/26 by Stefan Schreieder, Schreieder, Stefan
Mathematics · #14C15 #14C25 #14C35 #Advanced Topology and Set Theory #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #K-Theory and Homology (math.KT) #Number Theory (math.NT) #Rings, Modules, and Algebras

paper · pdf · doi:10.48550/arxiv.2406.18706

openalex publication_date 2024/06/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

We show that the Tate conjecture for divisors over a finite field \mathbb F is equivalent to an explicit algebraic problem about the third Milnor K-group of the function field \mathbb F(x,y,z) in three variables over \mathbb F.

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