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Unstable algebraic K-theory: homological stability and other observations

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arxiv 2405.02065 v2 pith:UHH73ZWI submitted 2024-05-03 math.KT

Mikala {O}rsnes Jansen This is my paper · ORCID
classification math.KT
keywords algebraick-theorystabilityhomologicalmodelpropertiestheyunstable
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We investigate stability properties of the reductive Borel-Serre categories; these were introduced as a model for unstable algebraic K-theory in previous work. We see that they exhibit better homological stability properties than the general linear groups. We also show that they provide an explicit model for Yuan's partial algebraic K-theory.

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  1. A chromatic approach to homological stability

    math.AT 2025-08 accept novelty 8.0 of 10

    Under mild axioms on a graded E2-algebra over a positive-characteristic field, higher-order homological stability maps exist with slopes approaching 1, and the patterns are governed by a stability Hopf algebra.

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