Global Units Modulo Elliptic Units and 2-Ideal Class Groups

Details Global Units Modulo Elliptic Units and 2-Ideal Class Groups Global Units Modulo Elliptic Units and 2-Ideal Class Groups

2011-02-15

arxiv.org/abs/1102.3031v1

Mathematics

Number Theory

16 pages

Scientific paper

Let p\in\{2,3\}, and let k be an imaginary quadratic field in which p decomposes into two distinct primes \mathfrak{p} and \bar{\mathfrak{p}}. Let k_\infty be the unique Z_p-extension of k which is unramified outside of \mathfrak{p}, and let K_\infty be a finite extension of k_\infty, abelian over k. We prove that in K_\infty, the projective limit of the p-class group and the projective limit of units modulo elliptic units share the same \mu-invariant and the same \lambda-invariant. Then we prove that up to a constant, the characteristic ideal of the projective limit of the p-class group coincides with the characteristic ideal of the projective limit of units modulo elliptic units.

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