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Non-commutative iwasawa theory for d-Fold false tate extensions

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posted on 23.02.2017 by Peters, Lloyd Christopher
For the (d+1)-dimensional Lie group G=Z_p^{ imes}ltimes Z_p^{oplus d}, we determine through the use of p-power congruences, a necessary and sufficient set of conditions whereby a collection of abelian p-adic L-functions arises from an element in K_1(Z_p[[G]]). We construct an additive theta map which produces additive p-power congruences, and then using the Taylor Oliver logarithm, we arrive at a multiplicative version of these congruences. If E is a semistable elliptic curve over Q with good ordinary reduction at p, the abelian p-adic L-functions already exist, therefore one can predict many new families of higher order congruences. The first layer congruences are then verified computationally in a variety of cases. The final chapter contains computations for elliptic curves with bad multiplicative reduction at p, that the author performed for Delbourgo and Lei in [10]. All of the computations were done using the package MAGMA.

History

Campus location

Australia

Principal supervisor

Daniel Delbourgo

Year of Award

2014

Department, School or Centre

Mathematical Sciences

Faculty

Faculty of Science

Exports