@article{74f719b84de84bb8ba33d27e9d3fe67a,
title = "Algebraic K -theory and Grothendieck–Witt theory of monoid schemes",
abstract = "We study the algebraic K-theory and Grothendieck–Witt theory of proto-exact categories of vector bundles over monoid schemes. Our main results are the complete description of the algebraic K-theory space of an integral monoid scheme X in terms of its Picard group Pic(X) and pointed monoid of regular functions Γ (X, OX) and a complete description of the Grothendieck–Witt space of X in terms of an additional involution on Pic(X). We also prove space-level projective bundle formulae in both settings.",
keywords = "Algebraic K-theory, Grothendieck–Witt theory, Monoid schemes, Projective bundle formula",
author = "Eberhardt, {Jens Niklas} and Oliver Lorscheid and Young, {Matthew B.}",
note = "Funding Information: The authors thank Marco Schlichting for helpful correspondence and an anonymous referee for useful feedback. All three authors thank the Max Planck Institute for Mathematics in Bonn for its hospitality and financial support. This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/ ), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. Publisher Copyright: {\textcopyright} 2021, The Author(s).",
year = "2022",
month = jun,
doi = "10.1007/s00209-021-02919-z",
language = "English",
volume = "301",
pages = "1407--1445",
journal = "Mathematische zeitschrift",
issn = "0025-5874",
publisher = "Springer",
number = "2",
}