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• W1489661707 abstract "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." @default.
• W1489661707 created "2016-06-24" @default.
• W1489661707 creator A5070989333 @default.
• W1489661707 date "2007-04-16" @default.
• W1489661707 modified "2023-09-27" @default.
• W1489661707 title "New Approach to Arakelov Geometry" @default.
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