On $p$-adic intermediate Jacobians
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- by Wayne Raskind and Xavier Xarles PDF
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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.References
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Additional Information
- Wayne Raskind
- Affiliation: Department of Mathematics, University of Southern California, Los Angeles, California 90089-2532
- MR Author ID: 213137
- 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
- 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 - © Copyright 2007
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Trans. Amer. Math. Soc. 359 (2007), 6057-6077
- MSC (2000): Primary 14K30; Secondary 14K99, 14F20
- DOI: https://doi.org/10.1090/S0002-9947-07-04246-8
- MathSciNet review: 2336316