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Transcendence of Hecke operators in the big Hecke algebra

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We prove a transcendence result of Hecke operator T.(l) over the ring generated by diamond operators over ℚ in a non-CM component of the cyclotomic ordinary big p-adic Hecke algebra, and we discuss its conjectural implication of a modulo-p version to the vanishing of the cyclotomic μ-invariant. © 2014.

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