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math.KT2026
Mixed Tate motives over number fields
Alexander Kupers, Daniil Rudenko, Ismael Sierra
This paper relates algebraic K-theory of fields to polylogarithms via general linear groups. We focus on the case of number fields and prove that the motivic realisation map from t…
math.KT2026
The Goncharov Lie coalgebra of a field
Alexander Kupers, Daniil Rudenko, Ismael Sierra
This paper relates algebraic -theory of fields to polylogarithms via general linear groups. We introduce the Goncharov Lie coalgebra, defined in terms of the -homology…
math.KT2025
A stable rank filtration on direct sum -theory
Jonathan Campbell, Alexander Kupers, Inna Zakharevich
In the literature, there are two standard rank filtrations on -theory: an ``unstable'' one which is traditionally defined through the homology of , and a ``stable'' one wh…