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In this paper we prove the p-adic analogue of a result of Hamida [11], namely that the p-adic Borel regulator introduced by Huber and Kings for the K-theory of a p-adic number field equals Karoubi's p-adic regulator up to an explicit rational factor.

We derive a power series formula for the p-adic regulator on the higher dimensional algebraic K-groups of number fields. This formula is designed to be well suited to computer calculations and to reduction modulo powers of p.

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 Soulé regulator. On the way we give a new description of the Lazard isomorphism for certain formal groups. We also show that the Soulé regulator is induced by continuous and even analytic classes.

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Comparison of Karoubi's regulator and the p-adic Borel regulator

p-adic cocycles and their regulator maps

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

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3 results

Comparison of Karoubi's regulator and the p-adic Borel regulator

p-adic cocycles and their regulator maps

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