Abstract
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.
Dedicated to the memory of Robert Coleman
Mathematics Subject Classification (2010). 11G05; 11G07; 11G40; 11R23; 14G10.
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Büyükboduk, K. (2017). p-adic Variation in Arithmetic Geometry: A Survey. In: Mourtada, H., Sarıoğlu, C., Soulé, C., Zeytin, A. (eds) Algebraic Geometry and Number Theory . Progress in Mathematics, vol 321. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-47779-4_1
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DOI: https://doi.org/10.1007/978-3-319-47779-4_1
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