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• W3206007716 endingPage "370" @default.
• W3206007716 startingPage "327" @default.
• W3206007716 abstract "The main goal of this expository article is to survey recent progress on the arithmetic Siegel–Weil formula and its applications. We begin with the classical sum of two squares problem and put it in the context of the Siegel–Weil formula. We then motivate the geometric and arithmetic Siegel–Weil formula using the classical example of the product of modular curves. After explaining the recent result on the arithmetic Siegel–Weil formula for Shimura varieties of arbitrary dimension, we discuss some aspects of the proof and its application to the arithmetic inner product formula and the Beilinson–Bloch conjecture. Rather than being intended as a complete survey of this vast field, this article focuses more on examples and background to provide easier access to several recent works by the author with W. Zhang and Y. Liu." @default.
• W3206007716 created "2021-10-25" @default.
• W3206007716 creator A5003753200 @default.
• W3206007716 date "2023-01-17" @default.
• W3206007716 modified "2023-09-26" @default.
• W3206007716 title "From sum of two squares to arithmetic Siegel–Weil formulas" @default.
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