Abstract
We give a geometric description of the unit root splitting of the Hodge filtration of the first de Rham cohomology of an ordinary Abelian variety over a local field, as the splitting determined by a formal completion of the universal vectorial extension of the Abelian variety.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
R. Coleman,Duality for de Rham cohomology of Abelian schemes, to appear.
R. Coleman and A. Iovita,Frobenius and monodromy operators for curves and Abelian varieties, Duke Mathematical Journal97 (1999), 171–215.
R. Coleman and A. Iovita,Frobenius and monodromy operators on curves via degeneration, in preparation.
R. Coleman,The universal vectorial bi-extension and p-adic heights, Inventiones Mathematicae103 (1991), 631–650.
J.A. Dieudonné and A. Grothendieck,Éléments de Géometrie Algébrique I, Springer-Verlag, Berlin, 1971.
J. M. Fontaine,Représentations p-adiques semi-stables, Asterisque223 (1994), exposé III, 113–185.
P. Gabriel and M. Demazure,Groupes Algèbriques, North-Holland, Amsterdam, 1970.
O. Hyodo and K. Kato,Semi-stable reduction and crystalline cohomology with logarithmic poles, Asterisque223 (1994), exposé V, 221–269.
L. Illusie,Reduction semi-stable ordinarire, cohomologie étale p-adique et cohomologie de de Rham d’après Bloch-Kato et Hyodo, Appendice à l’exposé IV, Asterisque223 (1994), 209–220.
N. Katz,Crystalline cohomology, Dieudonné modules and Jacobi sums, Automorphic forms, representation theory and arithmetic (Bombay, 1979), Tata Institute of Fundamental Research Studies in Mathematics, 10, Bombay, 1981, pp. 165–246.
B. Le Stum,Cohomologie Rigide et Variété Abéliennes, PhD thesis, Université de Rennes I, 1985 (unpublished).
B. Mazur and W. Messing,Universal extensions and one dimensional crystalline cohomology, Lecture Notes in Mathematics370, Springer-Verlag, Berlin, 1974.
W. Messing,The universal vectorial extension of an abelian variety by a vector group, Symposia in Mathematics11 (1973), 359–372.
D. Mumford,Abelian Varieties, Oxford University Press, 1988.
T. Tsuji,p-Adic Hodge theory in the semi-stable reduction case, Proceedings of the International Congress of Mathematics, Vol. II, Berlin, 1998.
Y. I. Zarhin,p-adic heights on abelian varieties, inSéminaire de Théorie des Nombres, Paris 1997–8, Progress in Mathematics81 (1990), 317–341.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Iovita, A. Formal sections and de Rham cohomology of semistable Abelian varieties. Isr. J. Math. 120, 429–447 (2000). https://doi.org/10.1007/BF02834846
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/BF02834846