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摘要翻译：
这一工作致力于一种新的完全代数方法来研究Arakelov几何，它不要求所考虑的变化是一般光滑的或射影的。为了建立这样一种方法，我们发展了广义环和方案理论，它包括经典环和方案以及诸如F_1（“单元场”）、Z_\infty（“实数”）、T（热带数）等“奇异”对象，从而提供了研究这些对象的系统方法。这种广义环和方案的理论发展到代数K-理论、交理论和Chern类的构造。然后证明了Q上代数簇的Arakelov模型的存在性，并将我们的一般结果应用于此类模型。
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英文标题：
《New Approach to Arakelov Geometry》
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作者：
Nikolai Durov (Max Planck Institute for Mathematics, St.Petersburg
State University)
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最新提交年份：
2007
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分类信息：
一级分类：Mathematics 数学
二级分类：Algebraic Geometry 代数几何
分类描述：Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology
代数簇，叠，束，格式，模空间，复几何，量子上同调
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一级分类：Mathematics 数学
二级分类：Number Theory 数论
分类描述：Prime numbers, diophantine equations, analytic number theory, algebraic number theory, arithmetic geometry, Galois theory
素数，丢番图方程，解析数论，代数数论，算术几何，伽罗瓦理论
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英文摘要：
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.
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PDF链接：
https://arxiv.org/pdf/0704.2030
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