Abstract
Let p be a prime number. Let K be an abelian number field with p ∤ [K : ℚ] and ζp ∈ K, K∞/K the cyclotomic ℤp-extension, and Kn the nth layer with K0 = K. Let $\mathcal U$n be the group of semi-local principal units of Kn at the prime p, and $\mathcal U$n(1) the elements u of $\mathcal U$n satisfying the congruence u ≣ 1 modulo ζp - 1. The Galois module structure of $\mathcal U$n is well understood. The purpose of this paper is to determine the Galois module structure of $\mathcal U$n(1).
Citation
Humio ICHIMURA. "Semi-local units at p of a cyclotomic ${\mathbb Z}_p$-extension congruent to 1 modulo $\zeta_p - 1$." Hokkaido Math. J. 44 (3) 397 - 407, October 2015. https://doi.org/10.14492/hokmj/1470053371
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