$K$-Theory of Cuspidal Curves Over a Perfectoid Base And Formal Analogues
Abstract
In this paper we continue the work of using the recent advances in algebraic $K$-theory to extend computations done in characteristic $p$ to the mixed characteristic setting using perfectoid rings. We extend the work of Hesselholt-Nikolaus in \cite{Hesselholt_Nikolaus} on the algebraic $K$-Theory of cuspidal curves. We consider both cuspidal curves and the $p$-completion of cuspidal curves. Along the way we also study the $K$-theory of the $p$-completed affine line over a perfectoid ring.
- Publication:
-
arXiv e-prints
- Pub Date:
- March 2022
- DOI:
- 10.48550/arXiv.2203.17136
- arXiv:
- arXiv:2203.17136
- Bibcode:
- 2022arXiv220317136R
- Keywords:
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- Mathematics - K-Theory and Homology;
- Mathematics - Algebraic Geometry;
- Mathematics - Algebraic Topology;
- 19D55(Primary);
- 55P91;
- 14G45(Secondary)
- E-Print:
- 27 pages. Comments welcome