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

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.Comment: 38 page

A cohomological Tamagawa number formula

For smooth linear group schemes over \bbZ we give a cohomological interpretation of the local Tamagawa measures as cohomological periods. This is in the spirit of the Tamagawa measures for motives defined by Bloch and Kato. We show that in the case of tori the cohomological and the motivic Tamagawa measures coincide, which reproves the Bloch-Kato conjecture for motives associated to tori.Comment: 20 pages, reference adde