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On higher Du Bois singularities and K-regularity
- Part of
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- Journal:
- Compositio Mathematica / Volume 162 / Issue 8 / August 2026
- Published online by Cambridge University Press:
- 13 October 2026, pp. 1818-1850
- Print publication:
- August 2026
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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.
Towards Vorst's conjecture in positive characteristic
- Part of
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- Journal:
- Compositio Mathematica / Volume 157 / Issue 6 / June 2021
- Published online by Cambridge University Press:
- 20 May 2021, pp. 1143-1171
- Print publication:
- June 2021
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Vorst's conjecture relates the regularity of a ring with the
$\mathbb {A}^{1}$-homotopy invariance of its 
$K$-theory. We show a variant of this conjecture in positive characteristic.
