A. Kupers

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math.KT2026

The Goncharov Lie coalgebra of a field

Alexander Kupers, Daniil Rudenko, Ismael Sierra

This paper relates algebraic $K$ -theory of fields to polylogarithms via general linear groups. We introduce the Goncharov Lie coalgebra, defined in terms of the $E_{\infty}$ -homology…

math.KT2025

A stable rank filtration on direct sum $K$ -theory

Jonathan Campbell, Alexander Kupers, Inna Zakharevich

In the literature, there are two standard rank filtrations on $K$ -theory: an ``unstable'' one which is traditionally defined through the homology of $G L_{n}$ , and a ``stable'' one wh…

The Goncharov Lie coalgebra of a field

A stable rank filtration on direct sum K-theory

A stable rank filtration on direct sum $K$ -theory