Low dimensional adelic geometry
Publication Date
July 18, 2019
Creator
Abstract
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.
Item Type
ethesis
Thesis Type
PhD
Supervisors
Subjects (LC)
Associated Schools / Departments
School of Mathematical Sciences (UK)
eprints ID
55728
UoN Repository URI
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Low_dim_adelic_geo.pdf
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