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P-adic variation in arithmetic geometry: a survey

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The main goal of this survey is to provide a general overview of the theme of p-adic variation, both from a historical and technical view point. We start off with Kummer’s work and Iwasawa’s treatment of cyclotomic fields, which eventually paved the way to the modern p-adic variational techniques. These methods have proved extremely powerful and enabled us to gain access to some of the most important problems in mathematics, such as the Bloch-Kato conjectures and Langlands’ Programme. We will point at a variety of concrete applications in this vein.

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Springer

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Mathematics

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Progress in Mathematics

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10.1007/978-3-319-47779-4_1

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