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March 2018 A regulator map for 1-cycles with modulus
Mirai Onoda
Kodai Math. J. 41(1): 167-200 (March 2018). DOI: 10.2996/kmj/1521424831

Abstract

Let $k$ be a field of characteristic 0. We define a map from the additive higher Chow group of 1-cycles with strong sup $m$-modulus $CH_1(A_k(m), n)_{ssup}$ to the module of absolute Kähler differentials of $k$ with twisted $k^*$-action $\Omega^{n-2}_k\langle \omega \rangle$ of weight $\omega$. We will call the map a regulator map, and we show that the regulator map is surjective if $k$ is an algebraically closed field. In case $\omega = m+1$, this map specializes to Park's regulator map. We study a relationship between the cyclic homology and the additive higher Chow group with strong sup modulus by using our regulator map.

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Mirai Onoda. "A regulator map for 1-cycles with modulus." Kodai Math. J. 41 (1) 167 - 200, March 2018. https://doi.org/10.2996/kmj/1521424831

Information

Published: March 2018
First available in Project Euclid: 19 March 2018

zbMATH: 06912408
MathSciNet: MR3777394
Digital Object Identifier: 10.2996/kmj/1521424831

Rights: Copyright © 2018 Tokyo Institute of Technology, Department of Mathematics

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Vol.41 • No. 1 • March 2018
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