On the K-theory of planar cuspical curves and a new family of polytopes

Let k be a regular Fp-algebra, let A = k[x,y]/(xb - ya) be the coordinate ring of a planar cuspical curve, and let I = (x,y) be the ideal that defines the cusp point. We evaluate the relative K-groups Kq(A,I) in terms of the groups of de Rham-Witt forms of k. The calculation is conditioned on a conjecture of a combinatorial nature which we formulate. The result generalizes previous results for K0 and K1 by Krusemeyer.

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