数作为函数：莫斯科algebraic geometry学派思想的发展
Numbers as functions: the development of an idea in the Moscow school of algebraic geometry
摘要：
这是作者在“Matériaux pour l 'Histoire des Mathématiques au XXème siècle”会议上发表的演讲的扩展文本，该会议于1996年1月在尼斯举行。任务是描述一个领域的发展算术代数几何在莫斯科在20世纪50年代和60年代。我们将从最简单的概念开始，解释数与函数之间的类比的意义。在第二部分中，我们研究了一个非平凡的例子：互易定律的显式公式。在第三部分中，我们将了解莫斯科学派“社会”生活的某些方面，特别是某些研讨会、讲座和书籍。在最后一部分，我们将研究这种类比的另一个例子：算术曲面和阿拉克洛夫理论。
英文摘要：
This is expanded text of a lecture delivered by the author at the conference "Matériaux pour l'Histoire des Mathématiques au XXème siècle", which took place in Nice in January 1996. The task was to describe one area in the development of arithmetical algebraic geometry in Moscow during the 1950s and 1960s. We shall begin by explaining the meaning of the analogy between numbers and functions, starting with the simplest concepts. In the second part we study a nontrivial example: the explicit formula for the law of reciprocity. In the third part we shall become acquainted with certain aspects of the "social" life of the Moscow school, in particular, with certain seminars, lectures, and books. In the final part we shall examine another example of this analogy: arithmetical surfaces and Arakelov theory.
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