New Approach to Arakelov Geometry
| dc.creator | Durov, Nikolai | |
| dc.date | 2007-04-16 | |
| dc.date.accessioned | 2026-07-07T07:56:44Z | |
| dc.date.available | 2026-07-07T07:56:44Z | |
| dc.description | This work is dedicated to a new completely algebraic approach to Arakelov geometry, which doesn't require the variety under consideration to be generically smooth or projective. In order to construct such an approach we develop a theory of generalized rings and schemes, which include classical rings and schemes together with "exotic" objects such as F_1 ("field with one element"), Z_\infty ("real integers"), T (tropical numbers) etc., thus providing a systematic way of studying such objects. This theory of generalized rings and schemes is developed up to construction of algebraic K-theory, intersection theory and Chern classes. Then existence of Arakelov models of algebraic varieties over Q is shown, and our general results are applied to such models. | |
| dc.description | 568 pages, with hyperlinks | |
| dc.identifier | https://arxiv.org/abs/0704.2030 | |
| dc.identifier | http://arxiv.org/abs/0704.2030 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/127421 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | Number Theory | |
| dc.subject | 14G40 (Primary), 14A20, 18G55, 08A40 (Secondary) | |
| dc.title | New Approach to Arakelov Geometry | |
| dc.type | text |