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P-adic Banach spaces and families of modular forms
Let p be a prime, Cp the completion of an algebraic closure of the p-adic numbers Qp and K a nite extension of Qp contained in Cp. Let v be the valuation on Cp such that v(p) = 1 and let | | be theExpand
Division values in local fields
Classical and overconvergent modular forms
The purpose of this article is to use rigid analysis to clarify the relation between classical modular forms and Katz’s overconvergent forms. In particular, we prove a conjecture of F. Gouvea [G,Expand
Torsion points on curves and p-adic Abelian integrals
THEOREM A. Let f: C --* J be an Albanese morphism defined over a number field K, of a s-mooth curve of genus g into its Jacobian. Suppose J has potential complex multiplication. Let S denote the setExpand
On the semi-simplicity of the $U_p$-operator on modular forms
For and positive integers, let denote the -vector space of cuspidal modular forms of level and weight . This vector space is equipped with the usual Hecke operators , . If we need to consider severalExpand
Stable Maps of Curves
Let h:X ! Y be a finite morphism of smooth connected complete curves over Cp. We show h extends to a finite morphism between semi-stable models of X and Y.
The Frobenius and monodromy operators for curves and abelian varieties
In this paper, we give explicit descriptions of Hyodo and Kato's Frobenius and Monodromy operators on the first $p$-adic de Rham cohomology groups of curves and Abelian varieties with semi-stableExpand