On the K-theory of coordinate axes in affine space
K-Theory and Homology
2021-03-10 v2 Algebraic Geometry
Number Theory
Abstract
Let k be a perfect field of characteristic p>0, let A_d be the coordinate ring of the coordinate axes in affine d-space over k, and let I_d be the ideal defining the origin. We evaluate the relative K-groups K_q(A_d,I_d) in terms of p-typical Witt vectors of k. When d=2 the result is due to Hesselholt, and for K_2 it is due to Dennis and Krusemeyer. We also compute the groups K_q(A_d,I_d) in the case where k is an ind-smooth algebra over the rationals, the result being expressed in terms of algebraic de Rham forms. When k is a field of characteristic zero this calculation is due to Geller, Reid and Weibel.
Keywords
Cite
@article{arxiv.1901.08550,
title = {On the K-theory of coordinate axes in affine space},
author = {Martin Speirs},
journal= {arXiv preprint arXiv:1901.08550},
year = {2021}
}
Comments
34 pages, updated with edits from referee report. To appear in Algebraic and Geometric Topology