arXiv subjects

Martin Speirs

Publications and source records attributed to Martin Speirs.

2 recordsLinked to original sources

arXiv2020

On the K-theory of coordinate axes in affine space

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.

math.KT↗

arXiv2020

On the K-theory of truncated polynomial algebras, revisited

We revisit the computation, due to Hesselholt and Madsen, of the K-theory of truncated polynomial algebras for perfect fields of positive characteristic. The resulting K-groups are expressed in terms of big Witt vectors of the field. The original proof relied on an understanding of cyclic polytopes in order to determine the genuine equivariant homotopy type of the cyclic bar construction for a suitable monoid. Using the Nikolaus-Scholze framework for topological cyclic homology we achieve the same result using only the homology of said cyclic bar construction, as well as the action of Connes' operator.

math.KT↗