### Algebraic *K*-theory of planar cuspidal curves

In this paper, we evaluate the algebraic *K*-groups of a
planar cuspidal curve over a perfect **F**_{p}-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.

Lars Hesselholt
<larsh@math.nagoya-u.ac.jp>