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- W2070970828 abstract "Let p be an odd prime. Let k be an algebraic number field and let k˜ be the compositum of all the Zp-extensions of k, so that Gal(k˜/k)≃Zpd for some finite d. We shall consider fields k with Gal(k/Q)≃(Z/2Z)n. Building on known results for quadratic fields, we shall show that the Galois group of the maximal abelian unramified pro-p-extension of k˜ is pseudo-null for several such k's, thus confirming a conjecture of Greenberg. Moreover we shall see that pseudo-nullity can be achieved quite early, namely in a Zp2-extension, and explain the consequences of this on the capitulation of ideals in such extensions." @default.
- W2070970828 created "2016-06-24" @default.
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- W2070970828 date "2007-01-01" @default.
- W2070970828 modified "2023-09-29" @default.
- W2070970828 title "Greenberg's conjecture and capitulation in <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML altimg=si1.gif overflow=scroll><mml:msubsup><mml:mi mathvariant=double-struck>Z</mml:mi><mml:mi>p</mml:mi><mml:mi>d</mml:mi></mml:msubsup></mml:math>-extensions" @default.
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- W2070970828 doi "https://doi.org/10.1016/j.jnt.2006.04.004" @default.
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