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Compositio Mathematica Compositio Mathematica

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Ordinary p-adic étale Cohomology Groups Attached to Towers of Elliptic Modular Curves

Published online by Cambridge University Press:  04 December 2007

MASAMI OHTA
MASAMI OHTA
Affiliation:
Department of Mathematics, Tokai University, Hiratsuka, Kanagawa, 259-12, Japan
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Abstract

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Fix a prime number p [ges ] 5 and a positive integer N prime to p. We consider the projective limits of p-adic étale cohomology groups of the modular curves X1(Npr) and Y1(Npr) (r [ges ] 1), which are denoted by ESp(N) ${\biib Z}$p and GES p(N)${\biib Z}$p, respectively. Let e* ′ be the projector to the direct sum of the ωi-eigenspaces of the ordinary part, for i [nequiv ] 0, −1 mod p−1. Our main result states that e* ′ GESp (N)${\biib Z}$p has a good p-adic Hodge structure, which can be described in terms of λ-adic modular forms, extending the previously known result for e*′ ESp (N)${\biib Z}$p. We then apply the method of Harder and Pink to the Galois representation on e*′ ESp(N) ${\biib Z}$p to construct large unramified abelian p-extensions over cyclotomic ${\bib Z}$p-extensions of abelian number fields.

Keywords

Eichler–Shimura cohomologyA-adic modular formscyclotomic fields.
Type
Research Article
Information
Compositio Mathematica , Volume 115 , Issue 3 , February 1999 , pp. 241 - 301
Copyright
© 1999 Kluwer Academic Publishers
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