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On higher Du Bois singularities and $K$-regularity
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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.
Forward citations
Cited by 2 Pith papers
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Negative $K$-theory and Hodge theory
For complex varieties with klt or rational singularities, negative K-theory is shown to be governed by mixed Hodge weights and higher singularity types, with new proof in dimension three and partial results in dimension four.
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Negative $K$-theory and Hodge theory
Negative K-groups of complex varieties are analyzed via mixed Hodge theory, higher singularities, Chow groups, and the Minimal Model Program.
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