Bloch and Kato's exponential map: three explicit formulas

Details Bloch and Kato's exponential map: three explicit formulas Bloch and Kato's exponential map: three explicit formulas

2002-09-21

arxiv.org/abs/math/0209283v1

Documenta Mathematica 2003, Kazuya Kato's fiftieth birthday. Extra Vol., 99--129.

Mathematics

Number Theory

22 pages, in english

Scientific paper

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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