Abstract
This thesis consists of two closely related projects concerning the structure of the universal lifting ring of a mod p representation of the Galois group of a p-adic local field. The first project, originally written in the published paper [Iye20], is the sole work of the author and focuses only on the trivial mod p representation. Under some mild conditions on p and the dimension, we prove that the universal lifting ring is a complete intersection of expected dimension with normal generic fibre and classify its irreducible components. The second project, originally written in the arXiv preprint [BIP21], was conceived and completed jointly with Gebhard B¨ockle and Vytautas Paˇsk¯unas. It strengthens and generalizes the previous result to all mod p Galois representations, unconditionally. The first project was completed before the second project was started, and though there is some overlap in ideas between the two projects, the methods used are substantially different.Some terminology and notation has been slightly changed from [Iye20] and [BIP21] for internal consistency and readability of this thesis. The mathematical content is the same, except for some minor corrections to the published paper [Iye20].
| Date of Award | 1 Dec 2022 |
|---|---|
| Original language | English |
| Awarding Institution |
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| Supervisor | Fred Diamond (Supervisor), affiliated academic (Supervisor), Fred Diamond (Supervisor) & affiliated academic (Supervisor) |