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Stable lattices in modular Galois representations and Hida deformation (1801.06961v3)
Published 22 Jan 2018 in math.NT
Abstract: In this paper, we discuss the variation of the numbers of the isomorphic classes of stable lattices when the weight and the level varies in a Hida deformation by using the Kubota-Leopoldt $p$-adic $L$-function. As a corollary, we give a sufficient condition for the numbers of the isomorphic classes of stable lattices in Hida deformation to be infinite.
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