Search

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].

Assessing developmental differences in children can be challenging. Two of the key stages in the assessment process are identification and formal assessment. This dissertation seeks to explore some of the forms of information, including symptom profiles, which contribute these assessment practices. Specifically, this dissertation focuses on three developmental conditions: autism spectrum disorder (ASD), attention deficit hyperactivity disorder (ADHD), and attachment-related conditions. This work is designed to reflect a hypothetical child or family’s pathway through services starting with a query of ASD, moving to differential conceptualisation of ADHD and attachment-related difficulties. First, a systematic review identified that GPs had variable knowledge of autism and sometimes leaned on lay sources. Qualitative interviews helped to identify some of the implicit forms of information that GPs draw on in their assessments (e.g. familiarity with the family). Analysis of qualitative interviews also identified the different forms of information that specialists use to inform decisions. In general, specialists tended to speak about the application of diagnosis in “natural” and “pragmatic” terms. That is, some children’s behaviour was a ‘natural-fit’ with diagnostic criteria, whereas the decision to diagnose, or indeed remove a diagnosis, from some children was grounded in pragmatic considerations. A conceptual review explored how attachment concepts are used in ASD and ADHD literature, which include a critical analysis of the Coventry Grid Interview, a tool which seeks to delineate symptom profiles of ASD and attachment difficulties. Qualitative interviews showed that suspicions about attachment tend to be raised by contextual factors and there were also some clear divergences between the developmental and clinical attachment theory discourses. Analysis of the Strengths and Difficulties Questionnaire (SDQ) provided further insight into the symptom profiles of children with ASD, ADHD, and attachment-related conditions, showing differences between subscales, but not in terms of total difficulties or networks of symptoms. The role of clinical judgment in assessments is often acknowledged, but rarely expanded upon. Taken together, this work illuminates some of the forms of information that shape these judgments. By foregrounding these forms of information, this work is well placed to contribute to the sociological, psychometric and applied literature on these topics. In addition, tensions were identified between various stakeholders. Recommendations for next steps include the integration of electronic healthcare records and the development of expert statements on neurodevelopment and attachment.