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arXiv · 2504.12402

On higher Du Bois singularities and $K$-regularity

Wanchun Shen
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Abstract

We study the relationship between higher Du Bois singularities and $K$-regularity, a notion that measures the $\mathbb{A}^1$-invariance of the algebraic $K$-groups. Building on this relationship, we establish a strengthened form of Vorst's conjecture for local complete intersections in characteristic zero. Our work also provides tools to construct new examples that illustrate various phenomena in the study of $K$-regularity. The main inputs for our results are vanishing theorems for the Du Bois complexes.

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Wanchun Shen. 2025-04-16. On higher Du Bois singularities and $K$-regularity. https://arxiv.org/abs/2504.12402

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