Osaka Journal of Mathematics

Polylogarithmic analogue of the Coleman-Ihara formula, I

Hiroaki Nakamura, Kenji Sakugawa, and Zdzisław Wojtkowiak

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The Coleman-Ihara formula expresses Soule's $p$-adic characters restricted to $p$-local Galois group as the Coates-Wiles homomorphism multiplied by $p$-adic $L$-values at positive integers. In this paper, we show an analogous formula that $\ell$-adic polylogarithmic characters for $\ell=p$ restrict to the Coates-Wiles homomorphism multiplied by Coleman's $p$-adic polylogarithms at any roots of unity of order prime to $p$.

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Osaka J. Math., Volume 54, Number 1 (2017), 55-74.

First available in Project Euclid: 3 March 2017

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Zentralblatt MATH identifier

Primary: 11G55: Polylogarithms and relations with $K$-theory
Secondary: 14H30: Coverings, fundamental group [See also 14E20, 14F35] 11S31: Class field theory; $p$-adic formal groups [See also 14L05] 11R18: Cyclotomic extensions


Nakamura, Hiroaki; Sakugawa, Kenji; Wojtkowiak, Zdzisław. Polylogarithmic analogue of the Coleman-Ihara formula, I. Osaka J. Math. 54 (2017), no. 1, 55--74.

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