On the motivic cohomology of some singular rings

Tess Bouis

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arXiv · 2608.05220

On the motivic cohomology of some singular rings

Tess Bouis

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Abstract

Using non-$\mathbb{A}^1$-invariant motivic cohomology, we prove motivic refinements of certain known computations of the algebraic $K$-theory of singular rings, such as rings of the form $\mathbb{Z}/p^n$, $\mathbb{Z}[x]/(x^e)$, and $\mathscr{C}(X;\mathbb{C})$ for $X$ a compact Hausdorff space. These refinements are made possible by the use of integral $p$-adic Hodge theory, as a replacement for the standard use of trace methods in $K$-theory.

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BibTeX RIS

Tess Bouis. 2026-08-05. On the motivic cohomology of some singular rings. https://arxiv.org/abs/2608.05220

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