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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

On $ p$-adic intermediate Jacobians


Authors: Wayne Raskind and Xavier Xarles
Journal: Trans. Amer. Math. Soc. 359 (2007), 6057-6077
MSC (2000): Primary 14K30; Secondary 14K99, 14F20
Published electronically: June 13, 2007
MathSciNet review: 2336316
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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\leq i\leq d$, we define a rigid analytic torus $ J^i(X)$ together with an Abel-Jacobi mapping to it from the Chow group $ CH^i(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 $ \bf {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.


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Additional Information

Wayne Raskind
Affiliation: Department of Mathematics, University of Southern California, Los Angeles, California 90089-2532
Email: raskind@math.usc.edu

Xavier Xarles
Affiliation: Departament de Matemàtiques, Universitat Autònoma de Barcelona, 08193 Bella- terra, Barcelona, Spain
Email: xarles@mat.uab.es

DOI: http://dx.doi.org/10.1090/S0002-9947-07-04246-8
PII: S 0002-9947(07)04246-8
Received by editor(s): May 23, 2005
Received by editor(s) in revised form: November 6, 2005
Published electronically: June 13, 2007
Additional Notes: The first author was partially supported by NSF grant 0070850, SFB 478 (Münster), CNRS France, and sabbatical leave from the University of Southern California
The second author was partially supported by grant PMTM2006-11391 from DGI
Article copyright: © Copyright 2007 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.