New Approach to Arakelov Geometry

dc.creatorDurov, Nikolai
dc.date2007-04-16
dc.date.accessioned2026-07-07T07:56:44Z
dc.date.available2026-07-07T07:56:44Z
dc.descriptionThis 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.description568 pages, with hyperlinks
dc.identifierhttps://arxiv.org/abs/0704.2030
dc.identifierhttp://arxiv.org/abs/0704.2030
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/127421
dc.subjectAlgebraic Geometry
dc.subjectNumber Theory
dc.subject14G40 (Primary), 14A20, 18G55, 08A40 (Secondary)
dc.titleNew Approach to Arakelov Geometry
dc.typetext

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