Greenberg's conjecture and units in multiple Zp-extensions
William G. McCallum
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 Zp-extensions a theorem of Iwasawa on the Kummer extension of the cyclotomic Zp-extension generated by p-power roots of units .
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