2019/03/20 by Lars Hesselholt, Thomas Nikolaus, Hesselholt, Lars +1
Mathematics · #Advanced Combinatorial Mathematics #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #K-Theory and Homology (math.KT) #math.KT
paper · pdf · doi:10.48550/arxiv.1903.08295
9 pages
openalex publication_date 2019/03/20 · arxiv created 2019/07/17 · arxiv updated 2019/07/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we evaluate the algebraic K-groups of a planar cuspidal curve over a perfect \mathbbFp-algebra relative to the cusp point. A conditional calculation of these groups was given earlier by Hesselholt, assuming a conjecture on the structure of certain polytopes. Our calculation here, however, is unconditional and illustrates the advantage of the new setup for topological cyclic homology by Nikolaus-Scholze, which is used throughout. The only input necessary for our calculation is the evaluation by the Buenos Aires Cyclic Homology group and by Larsen of the structure of Hochschild complex of the coordinate ring as a mixed complex, that is, as an object of the infinity category of chain complexes with circle action.