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This paper is a sequel to "Exponential periods and o-minimality I" that the authors wrote together with Philipp Habegger. We complete the comparison between different definitions of exponential periods, and show that they all lead to the same notion. In the first paper, we show that naive exponential periods are absolutely convergent exponential periods. We also show that naive exponential periods are up to signs volumes of definable sets in the o-minimal structure generated by $\mathbb{Q}$, the real exponential function and ${\sin}|_{[0,1]}$. In this paper, we compare these definitions with cohomological exponential periods and periods of exponential Nori motives. In particular, naive exponential periods are the same as periods of exponential Nori motives, which justifies that the definition of naive exponential periods singles out the correct set of complex numbers to be called exponential periods., Comment: The paper was merged with part I. See arXiv:2007.08280 for updates

These are extended abstracts from an series of lectures in 1997. The text has not been updated since then. We explain the construction of the motivic polylog as published in Annette Huber, J��rg Wildeshaus, Classical Motivic Polylogarithm According to Beilinson and Deligne, Doc.Math.J.DMV 3 (1998) 27-133. The main application is a comparison result for cyclotomic elements needed in the proof of the Tamagawa number conjecture of Bloch and Kato for Dirichlet characters. The exposition concentrates on the Hodge theoretic part of the story.

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 pages