Let be a perfect field of characteristic , let be the coordinate ring of the coordinate axes in affine –space over , and let be the ideal defining the origin. We evaluate the relative –groups in terms of –typical Witt vectors of . When the result is due to Hesselholt, and for it is due to Dennis and Krusemeyer. We also compute the groups in the case where is an ind-smooth algebra over the rationals, the result being expressed in terms of algebraic de Rham forms. When is a field of characteristic zero this calculation is due to Geller, Reid and Weibel.
"On the $K$–theory of coordinate axes in affine space." Algebr. Geom. Topol. 21 (1) 137 - 171, 2021. https://doi.org/10.2140/agt.2021.21.137