Polylogarithmic analogue of the Coleman-Ihara formula, I

Abstract

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 $p$.

References in corpus (2)

• p-adic multiple zeta values I -- p-adic multiple polylogarithms and the p-adic KZ equation
• On l-adic Galois L-functions

Cited by in corpus (2)

• On distribution formulas for complex and $\ell$-adic polylogarithms
• Finite and étale polylogarithms