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    Title      l  ON THE TATE MODULE OF A NUMBER FIELD
    Author   l  SOOGIL 
    Date   l  2013-09-12
    Category   l  ASARC-Prepint-13-06
    Download    l 1380003653_0.899208.pdf  
Abstract. Following Kuzmin, we investigate the Tate module of a number
eld k in terms of certain arithmetic properties of the p-units via class eld
theory. This gives rise to a relation of the Tate module of k with the conjectures
of Gross and Coates-Lichtenbaum as well as a question of Kato. We reduce the
Gross conjecture to the study of the universal norm subgroup of the p-units
over the cyclotomic Zp-extension and prove the Gross conjecture when the
number of primes of k dividing p is at most 2.

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