$K_2$-regularity and normality

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.

v2 12 pages. Added a result on the dimension of the singular set of local complete intersection du Bois singularities, communicated to us by Wanchun Shen. Added acknowledgements and declarations necessary for submission