Compositio Mathematica

, Volume 124, Issue 1, pp 57–63 | Cite as

Analytic Variation of p-adic Abelian Integrals

  • Roland Dreier
Article

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)ωP. In this paper, we prove that λω is locally analytic on S.

p-adic Abelian integrals algebraic families of curves locally analytic variation 

References

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    Coleman, R. F.: Torsion points on curves and p-adic Abelian integrals, Ann. of Math. 121 (1985), 111–168.Google Scholar
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    Faltings, G.: F-isocrystals on open varieties: Results and conjectures, In: The Grothendieck Festschrift, Vol. II, Birkhäuser, Boston, 1990, pp. 219–248.Google Scholar
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    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.Google Scholar
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    Zarhin, Y. G.: p-adic Abelian integrals and commutative Lie groups, J. Math. Sci. 81(3), 1996, 2744–2750. Algebraic Geom. 4.Google Scholar

Copyright information

© Kluwer Academic Publishers 2000

Authors and Affiliations

  • Roland Dreier
    • 1
  1. 1.Department of MathematicsOklahoma State UniversityStillwaterU.S.A.

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