Abstract
In Ann. of Math. 121 (1985), 111–168, Coleman defines p-adic Abelian integrals on curves. Given a family of curves X/S, a differential ω and two sections s and t, one can define a function λω on S by λω(P)=\({\int {}}\) s(P) t(P)ω P . In this paper, we prove that λω is locally analytic on S.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Coleman, R. F.: Torsion points on curves and p-adic Abelian integrals, Ann. of Math. 121 (1985), 111–168.
Faltings, G.: F-isocrystals on open varieties: Results and conjectures, In: The Grothendieck Festschrift, Vol. II, Birkhäuser, Boston, 1990, pp. 219–248.
Katz, N. M.: Travaux de Dwork, In: Séminaire Bourbaki, 24ème année, Exp. No. 409. Lecture Notes in Math. 317, Springer-Verlag, New York, 1972, pp. 167–200.
Zarhin, Y. G.: p-adic Abelian integrals and commutative Lie groups, J. Math. Sci. 81(3), 1996, 2744–2750. Algebraic Geom. 4.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Dreier, R. Analytic Variation of p-adic Abelian Integrals. Compositio Mathematica 124, 57–63 (2000). https://doi.org/10.1023/A:1002432618607
Issue Date:
DOI: https://doi.org/10.1023/A:1002432618607