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On the kernel and the image of the rigid analytic regulator in positive characteristic

2009/12/16 by Ambrus Pál, Ambrus Pal, Pal, Ambrus
Mathematics · #19D45 #19F27 #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometric and Algebraic Topology #K-Theory and Homology (math.KT) #Number Theory (math.NT) #math.KT #math.NT #msc:19D45 #msc:19F27

paper · pdf · doi:10.48550/arxiv.0912.3115

28 pages, to appear in Publ. Res. Inst. Math. Sci

arxiv created 2009/12/16 · openalex publication_date 2009/12/16 · arxiv updated 2010/01/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We will formulate and prove a certain reciprocity law relating certain residues of the differential symbol dlog2 from the K2 of a Mumford curve to the rigid analytic regulator constructed by the author in a previous paper. We will use this result to deduce some consequences on the kernel and image of the rigid analytic regulator analogous to some old conjectures of Beilinson and Bloch on the complex analytic regulator. We also relate our construction to the symbol defined by Contou-Carrere and to Kato's residue homomorphism, and we show that Weil's reciprocity law directly implies the reciprocity law of Anderson and Romo.

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