On generators of unramified Iwasawa module over an imaginary quadratic field

2023/03/20 by Tanaka, Takuya
#11R23 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2303.11119

Abstract

Let p be an odd prime number and k_p be the maximal pro-p extension unramified outside p of an imaginary quadratic field k. Let \widetildek be the maximal multiple ℤ_p extension over k and M_\widetildek be the maximal abelian pro-p extension unramified outside p over \widetildek. In this paper, we give an explicit description of a generating system of \rmGal(M_\widetildek/\widetildek) and study its structure. As an application, we apply it to describe the unramified Iwasawa module X_k for k.

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