On p-adic intermediate Jacobians

2006/01/17 by Wayne Raskind, Raskind, Wayne, Xavier Xarles +1
Mathematics · Medicine · #14F20 #14K30 #14K99 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Berberine and alkaloids research #FOS: Mathematics #Number Theory (math.NT) #math.AG #math.NT #msc:14F20 #msc:14K30 #msc:14K99

paper · pdf · doi:10.48550/arxiv.math/0601401

to appear in Transactions of the AMS

arxiv created 2006/01/17 · openalex publication_date 2006/01/17 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For an algebraic variety X of dimension d with totally degenerate reduction over a p-adic field (definition recalled below) and an integer i with 1≤ i≤ d, we define a rigid analytic torus Jⁱ(X) together with an Abel-Jacobi mapping to it from the Chow group CHⁱ(X)_hom of codimension i algebraic cycles that are homologically equivalent to zero modulo rational equivalence. These tori are analogous to those defined by Griffiths using Hodge theory over the complex numbers. We compare and contrast the complex and p-adic theories. Finally, we examine a special case of a p-adic analogue of the Generalized Hodge Conjecture

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