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Analytic Variation of p-adic Abelian Integrals

Published online by Cambridge University Press:  04 December 2007

Roland Dreier
Roland Dreier
Affiliation:
Department of Mathematics, Oklahoma State University, Stillwater, OK 74078, U.S.A. E-mail: droland@math.okstate.edu
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Abstract

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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.

Keywords

p-adic Abelian integralsalgebraic families of curveslocally analytic variation
Type
Research Article
Information
Compositio Mathematica , Volume 124 , Issue 1 , October 2000 , pp. 57 - 63
Copyright
© 2000 Kluwer Academic Publishers