Use this URL to cite or link to this record in EThOS: https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.754963
Title: On special elements for p-adic representations and higher rank Iwasawa theory at arbitrary weights
Author: Tsoi, Kwok-Wing
ISNI:       0000 0004 7427 9788
Awarding Body: King's College London
Current Institution: King's College London (University of London)
Date of Award: 2018
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Abstract:
In this thesis, we develop a theory of special elements in the higher exterior powers (or, more precisely, in the higher exterior power biduals) of the Galois cohomology of general p-adic representations over number fields. These elements constitute a natural extension of the concept of a ‘higher rank Euler system’ and we present evidence that they encode detailed information about the structure of Galois cohomology groups. In particular, we prove that a canonical ideal that one can define in terms of these elements is contained in both the relevant higher Fitting ideal and the annihilator ideal of the associated Galois cohomology group. In fact, under mild hypotheses, we find that the special elements completely determine the relevant higher Fitting ideal of the cohomology groups. Building upon this result, we are then able to determine the complete structure of the torsion part of the quotient of the higher exterior powers of the Galois cohomology group modulo the subgroup generated by the special elements. By means of a first concrete application, we specialise our theory to the p-adic represen-tations that arise from the Tate motives with cyclotomic twists. In this way, we both recover and refine the theory of generalised Stark elements recently developed by Burns, Kurihara and Sano. At the same time, we are able to answer a question explicitly raised by both Wash-ington and Lang regarding the Galois structure of global units modulo cyclotomic units in abelian fields, and also strongly refine a result of El Boukhari regarding the Galois structure of higher algebraic K-groups. In the same way, we can also formulate conjectures concerning p-adic L-series that have been formulated in other settings in earlier work of Castillo and Jones and of Solomon.
Supervisor: Burns, David John ; Kakde, Mahesh Ramesh Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID: uk.bl.ethos.754963  DOI: Not available
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