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arXiv · 2211.11110

$K$-Theory of Truncated Polynomials

Noah Riggenbach
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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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Noah Riggenbach. 2022-11-20. $K$-Theory of Truncated Polynomials. https://arxiv.org/abs/2211.11110

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