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Title: Low dimensional adelic geometry
Author: Dolce, Paolo
ISNI:       0000 0004 7965 6597
Awarding Body: University of Nottingham
Current Institution: University of Nottingham
Date of Award: 2019
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Adelic (and idelic) structures can be associated to algebraic and arithmetic varieties, and an adelic geometry can be developed as a bridge between algebraic geometry and arithmetic geometry. We study in detail adelic geometry in dimension one and two. In particular, such a theory can be seen as a generalisation of the theory of algebraic and arithmetic line bundles, so the result is a novel approach to intersection theory. The construction process of adelic objects is "from local to global" and it endows such objects with natural topologies. One of the main richnesses of adelic geometry is given by the topological interactions between adelic structures, and a deep study of them in the case of arithmetic surfaces might be crucial to the solution to higher number theory open problems.
Supervisor: Not available Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available
Keywords: QA440 Geometry