A $p$-adic analogue of the Borel regulator and the Bloch-Kato exponential map

Details A $p$-adic analogue of the Borel regulator and the Bloch-Kato exponential map A $p$-adic analogue of the Borel regulator and the Bloch-Kato exponential map

2006-12-20

arxiv.org/abs/math/0612611v1

Journal of the Institute of Mathematics of Jussieu, volume 10, issue 01, 2011, pp. 149-190

Mathematics

Number Theory

38 pages

Scientific paper

In this paper we define a $p$-adic analogue of the Borel regulator for the $K$-theory of $p$-adic fields. The van Est isomorphism in the construction of the classical Borel regulator is replaced by the Lazard isomorphism. The main result relates this $p$-adic regulator to the Bloch-Kato exponential and the Soul\'e regulator. On the way we give a new description of the Lazard isomorphism for certain formal groups.

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