K-Theory of Truncated Polynomials

2022/11/20 by Noah Riggenbach, Riggenbach, Noah
Mathematics · #Homotopy and Cohomology in Algebraic Topology #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models

paper · pdf · doi:10.48550/arxiv.2211.11110

Abstract

We study the algebraic K-theory of rings of the form R[x]/x^e. We do this via trace methods and filtrations on topological Hochschild homology and related theories by quasisyntomic sheaves. We produce computations for R a perfectoid ring in terms of the big Witt vectors of R, for R a smooth curve over a perfectoid ring in terms of the prismatic cohomology of R, and for R a complete mixed characteristic discrete valuation rings with perfect residue field in terms of the prismatic cohomology and Hodge-Tate divisor of R.

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