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The Syntomic Regulator for K2 of Curves with Arbitrary Reduction

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Arithmetic L-Functions and Differential Geometric Methods

Part of the book series: Progress in Mathematics ((PM,volume 338))

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Abstract

We give a formula for the syntomic regulator on K2 of a proper curve X over a p-adic field K. This generalizes the results of [Bes00c] where the curve was assumed to have good reduction. The formula is essentially the same with Coleman integration replaced by by Vologodsky integration.

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Besser, A. (2021). The Syntomic Regulator for K2 of Curves with Arbitrary Reduction. In: Charollois, P., Freixas i Montplet, G., Maillot, V. (eds) Arithmetic L-Functions and Differential Geometric Methods . Progress in Mathematics, vol 338. Birkhäuser, Cham. https://doi.org/10.1007/978-3-030-65203-6_3

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