Low dimensional adelic geometry

Dolce, Paolo (2019) Low dimensional adelic geometry. PhD thesis, University of Nottingham.

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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: Thesis (University of Nottingham only) (PhD)
Supervisors: Fesenko, Ivan B.
Keywords: Arakelov geometry, adeles, arithmetic geometry, algebraic geometry, intersection theory, surfaces
Subjects: Q Science > QA Mathematics > QA440 Geometry
Faculties/Schools: UK Campuses > Faculty of Science > School of Mathematical Sciences
Item ID: 55728
Depositing User: Dolce, Paolo
Date Deposited: 18 Jul 2019 04:40
Last Modified: 07 May 2020 12:02
URI: http://eprints.nottingham.ac.uk/id/eprint/55728

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