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

Wiley - 1999
Masami Ohta1
1Department of Mathematics, Tokai University, Hiratsuka, Kanagawa, Japan

Tóm tắt

Fix a prime number p ≥ 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 ≥ 1), which are denoted by ESp(N) Z p and GES p(N)Z p , respectively. Let e* ′ be the projector to the direct sum of the ωi-eigenspaces of the ordinary part, for i ≢ 0, -1 mod p-1. Our main result states that e* ′ GESp (N)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)Z p . We then apply the method of Harder and Pink to the Galois representation on e*′ ESp(N) Z p to construct large unramified abelian p-extensions over cyclotomic Z p -extensions of abelian number fields.

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