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Title: Interaction of topology and algebra in arithmetic geometry
Author: Camara, Alberto
ISNI:       0000 0004 2746 1923
Awarding Body: University of Nottingham
Current Institution: University of Nottingham
Date of Award: 2013
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This thesis studies topological and algebraic aspects of higher dimensional local fields and relations to other neighbouring research areas such as nonarchimedean functional analysis and higher dimensional arithmetic geometry. We establish how a higher local field can be described as a locally convex space once an embedding of a local field into it has been fixed. We study the resulting spaces from a functional analytic point of view: in particular we introduce and study bounded, c-compact and compactoid submodules of characteristic zero higher local fields. We show how these spaces are isomorphic to their appropriately topologized duals and study the implications of this fact in terms of polarity. We develop a sequential-topological study of rational points of schemes of finite type over local rings typical in higher dimensional number theory and algebraic geometry. These rings are certain types of multidimensional complete fields and their rings of integers and include higher local fields. Our results extend the constructions of Weil over (one-dimensional) local fields. We establish the existence of an appropriate topology on the set of rational points of schemes of finite type over the rings considered, study the functoriality of this construction and deduce several properties.
Supervisor: Not available Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available
Keywords: QA150 Algebra