Beilinson's Hodge Conjecture for K₁ revisited

2008/01/21 by Su-Jeong Kang, James D. Lewis, Kang, Su-Jeong +1
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Analytic Number Theory Research #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.0801.3236

openalex publication_date 2008/01/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let U be a smooth quasiprojective complex variety and CH^r(U,1) a special instance of Bloch's higher Chow groups. Jannsen was the first to show that the cycle class map cl_r,1 from CH^r(U,1) (tensored with Q) to hom_MHS(Q(0), H^2r-1(U,Q(r)) is not in general surjective, contradicting an earlier conjecture of Beilinson. In this paper, we give a refinement of Jannsen's counterexample, and further show that the aforementioned cycle class map becomes surjective at the generic point.

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