$K_2$-regularity and normality

TL;DR

This paper investigates the connection between K-regularity and scheme regularity, proving that K2-regular affine algebras over characteristic zero fields are normal and refining bounds for K-regularity in local complete intersections.

Contribution

It establishes that K2-regular affine algebras over characteristic zero fields are normal and improves existing bounds on K-regularity for local complete intersections.

Findings

K2-regular affine algebras over characteristic zero are normal

Improved K-regularity bounds for local complete intersections

Connections to higher du Bois singularities

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.