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    Title      l  On the tate module of a number field
    Author   l  SOOGIL SEO
    Date   l  2011-01-07
    Category   l  ASARC-Preprint-11-01
    Download    l 1294388101_0.555546.pdf  
Abstract. We investigate the order of vanishing of p-adic L function at s =
0 via class ¯eld theory. Our investigation gives rise to relations with Tate
modules of number ¯elds and connections to conjectures of Gross and Coates-
Lichtenbaum as well as a question of Kato. We reduce the conjecture to the
study of universal norm elements and norm comparable elements over the
cyclotomic Zp-extension. Based on examples and technical evidences, we are
lead to a conjecture on the Galois invariants of Tate module which is stronger
than the Gross conjecture.

Keyword

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