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Greenberg's conjecture and units in multiple Z_p-extensions

William G. McCallum
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Abstract

In this paper we prove Greenberg's pseudo-null conjecture for the field of p-th roots of unity in the case that p exactly divides the class number and the index of the global units in the local units. We also generalize to the case of multiple Z_p-extensions a theorem of Iwasawa on the Kummer extension of the cyclotomic Z_p-extension generated by p-power roots of units .

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William G. McCallum. 2000-07-13. Greenberg's conjecture and units in multiple Z_p-extensions. https://arxiv.org/abs/math/0007209

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