On p-adic intermediate jacobians

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 C. 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. © 2007 American Mathematical Society.