New Approach to Arakelov Geometry
New Approach to Arakelov Geometry
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DissertationPrüfungsdatum
25.06.2007Datum der Veröffentlichung
2007Erstgutachter
Faltings, GerdZweitgutachter
Harder, GünterMetadaten
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Inhalt
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.
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.
Klassifikation (DDC)
510 MathematikDurov, Nikolai: New Approach to Arakelov Geometry. - Bonn, 2007. - Dissertation, Rheinische Friedrich-Wilhelms-Universität Bonn.
Online-Ausgabe in bonndoc: https://nbn-resolving.org/urn:nbn:de:hbz:5N-11009
Online-Ausgabe in bonndoc: https://nbn-resolving.org/urn:nbn:de:hbz:5N-11009
@phdthesis{handle:20.500.11811/3110,
urn: https://nbn-resolving.org/urn:nbn:de:hbz:5N-11009,
author = {{Nikolai Durov}},
title = {New Approach to Arakelov Geometry},
school = {Rheinische Friedrich-Wilhelms-Universität Bonn},
year = 2007,
note = {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.},
url = {https://hdl.handle.net/20.500.11811/3110}
}
urn: https://nbn-resolving.org/urn:nbn:de:hbz:5N-11009,
author = {{Nikolai Durov}},
title = {New Approach to Arakelov Geometry},
school = {Rheinische Friedrich-Wilhelms-Universität Bonn},
year = 2007,
note = {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.},
url = {https://hdl.handle.net/20.500.11811/3110}
}
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