Non-commutative iwasawa theory for d-Fold false tate extensions
Peters, Lloyd Christopher
10.4225/03/58ae646d94556
https://bridges.monash.edu/articles/thesis/Non-commutative_iwasawa_theory_for_d-Fold_false_tate_extensions/4684399
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.
2017-02-23 04:26:20
P-adic L-functions
thesis(doctorate)
Iwasawa theory
1959.1/965406
ethesis-20140627-123910
Open access
2014
Elliptic curves
False tate extensions
monash:128548