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Bloch and Kato's exponential map: three explicit formulas

Laurent Berger
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Abstract

The purpose of this article is to give formulas for Bloch-Kato's exponential map and its dual for an absolutely crystalline p-adic representation V, in terms of the (phi,Gamma)-module associated to that representation. As a corollary of these computations, we can give a very simple (and slightly improved) description of Perrin-Riou's exponential map (which interpolates Bloch-Kato's exponentials for V(k)). This new description directly implies Perrin-Riou's reciprocity formula.

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Laurent Berger. 2002-09-21. Bloch and Kato's exponential map: three explicit formulas. https://arxiv.org/abs/math/0209283

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