Higher Du Bois singularities are shown to be equivalent, in many characteristic-zero settings, to K-regularity, yielding a strengthened Vorst conjecture for local complete intersections and a projective characterization of K-regularity.
$K_2$-regularity and normality
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abstract
We take a fresh look at the relationship between $K$-regularity and regularity of schemes, proving two results in this direction. First, we show that $K_2$-regular affine algebras over fields of characteristic zero are normal. Second, we improve on Vorst's $K$-regularity bound in the case of local complete intersections; this is related to recent work on higher du Bois singularities.
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On higher Du Bois singularities and $K$-regularity
Higher Du Bois singularities are shown to be equivalent, in many characteristic-zero settings, to K-regularity, yielding a strengthened Vorst conjecture for local complete intersections and a projective characterization of K-regularity.