Syntomic cohomology and Beilinson's Tate conjecture for K₂

2009/04/23 by Masanori Asakura, Asakura, Masanori, Kanetomo Sato +1 · 1 citation
Mathematics · #14C25 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.0904.3672

openalex publication_date 2009/04/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we study an analogue of the Tate conjecture for K₂ of U, the complement of split multiplicative fibers in an elliptic surface. A main result is to give an upper bound of the rank of the Galois fixed part of the etale cohomology H²(U,Q_p(2)). As an application, we give an elliptic K3 surface X over a p-adic field for which the torsion part of the Chow group CH₀(X) of 0-cycles is finite. This would be the first example of a surface X over a p-adic field whose geometric genus is non-zero and for which the torsion part of CH₀(X) is finite.

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