# Relative Chern Characters for Nilpotent Ideals

@inproceedings{Cortias2009RelativeCC,
title={Relative Chern Characters for Nilpotent Ideals},
author={Guillermo Corti{\~n}as and Charles A. Weibel},
year={2009}
}
If I is a nilpotent ideal in a $\mathbb{Q}$-algebra $A$, Goodwillie defined two isomorphisms from $K_*(A,I)$ to negative cyclic homology, $HN_*(A,I)$. One is the relative version of the absolute Chern character, and the other is defined using rational homotopy theory. The question of whether they agree was implicit in Goodwillie's 1986 Annals paper. In this paper, we show that the two isomorphisms agree. Here are three applications. 1.Cathelineau proved that the rational homotopy character is… CONTINUE READING

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