Greenberg's conjecture and units in multiple Z_p-extensions

Details Greenberg's conjecture and units in multiple Z_p-extensions Greenberg's conjecture and units in multiple Z_p-extensions

2000-07-13

arxiv.org/abs/math/0007209v1

Mathematics

Number Theory

Scientific paper

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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