A p-adic analogue of the Borel regulator

Guido Kings

Universitat Regensburg

Brandeis University

Thursday, March 1, 2007

Talk at 4:30 p.m. in 317 Goldsmith Hall

Tea at 4:00 p.m. in 300 Goldsmith Hall

Abstract: The Borel regulator plays an essential role in the study of special values of L-functions of number fields. To study integrality properties of these values one needs a good understanding of the p-adic regulator and the Bloch-Kato exponential map. In this talk we define a $p$-adic analogue of the Borel regulator for the $K$-theory of $p$-adic fields. After a review of Borel's construction, we show that one can replace the van Est isomorphism in Borel's regulator by the Lazard isomorphism to obtain an interesting theory. 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 and easy description of the Lazard isomorphism for certain formal groups.

Home Web page: Alexandru I. Suciu Posted: February 24, 2007
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