Low dimensional adelic geometry
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 g...
| Main Author: | |
|---|---|
| Format: | Thesis (University of Nottingham only) |
| Language: | English |
| Published: |
2019
|
| Subjects: | |
| Online Access: | https://eprints.nottingham.ac.uk/55728/ |
| _version_ | 1848799205403918336 |
|---|---|
| author | Dolce, Paolo |
| author_facet | Dolce, Paolo |
| author_sort | Dolce, Paolo |
| building | Nottingham Research Data Repository |
| collection | Online Access |
| description | 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. |
| first_indexed | 2025-11-14T20:31:58Z |
| format | Thesis (University of Nottingham only) |
| id | nottingham-55728 |
| institution | University of Nottingham Malaysia Campus |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-14T20:31:58Z |
| publishDate | 2019 |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | nottingham-557282025-02-28T14:19:44Z https://eprints.nottingham.ac.uk/55728/ Low dimensional adelic geometry Dolce, Paolo 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. 2019-07-18 Thesis (University of Nottingham only) NonPeerReviewed application/pdf en arr https://eprints.nottingham.ac.uk/55728/1/Low_dim_adelic_geo.pdf Dolce, Paolo (2019) Low dimensional adelic geometry. PhD thesis, University of Nottingham. Arakelov geometry adeles arithmetic geometry algebraic geometry intersection theory surfaces |
| spellingShingle | Arakelov geometry adeles arithmetic geometry algebraic geometry intersection theory surfaces Dolce, Paolo Low dimensional adelic geometry |
| title | Low dimensional adelic geometry |
| title_full | Low dimensional adelic geometry |
| title_fullStr | Low dimensional adelic geometry |
| title_full_unstemmed | Low dimensional adelic geometry |
| title_short | Low dimensional adelic geometry |
| title_sort | low dimensional adelic geometry |
| topic | Arakelov geometry adeles arithmetic geometry algebraic geometry intersection theory surfaces |
| url | https://eprints.nottingham.ac.uk/55728/ |