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

thesis

posted on 2017-02-23, 04:26 authored by Peters, Lloyd ChristopherFor 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

Mathematics## Course

Doctor of Philosophy## Degree Type

DOCTORATE## Faculty

Faculty of Science## Usage metrics

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