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    Title      l  ON ARITHMETIC PROPERTIES OF THE p-UNITS
    Author   l  SOOGIL SEO
    Date   l  2014-08-29
    Category   l  ASARC-Preprint-14-08
    Download    l 1409294017_0.455591.pdf  
Abstract. We define certain deviation modules for the Hasse local-global
norm theorem and Hilbert’s theorem 90 for the p-units over the cyclotomic Zp-
extension of a number field. We show that a necessary and sufficient condition
for the two deviations are isomorphic over all sufficiently large intermediate
fields in terms of an arithmetic property of the p-units which is called the
generalized Gross conjecture. The proof is based on deep results of Kuz’min
and Iwasawa on infinite class field theory. We will prove the Kuz’min’s main
result in a totally different way using the genus theory for p-ideal class group
which depends on cohomology theory rather than the infinite class field theory
used by Kuz’min and describe an explicit isomorphism.

Keyword

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