$K_2$-regularity and normality
Algebraic Geometry
2025-02-12 v2 K-Theory and Homology
Abstract
We take a fresh look at the relationship between -regularity and regularity of schemes, proving two results in this direction. First, we show that -regular affine algebras over fields of characteristic zero are normal. Second, we improve on Vorst's -regularity bound in the case of local complete intersections; this is related to recent work on higher du Bois singularities.
Keywords
Cite
@article{arxiv.2501.01567,
title = {$K_2$-regularity and normality},
author = {Christian Haesemeyer and Charles A. Weibel},
journal= {arXiv preprint arXiv:2501.01567},
year = {2025}
}
Comments
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