The regularity lemma is false over small fields
Rings and Algebras
2018-12-10 v1 Combinatorics
Abstract
The regularity lemma is a stringent condition of the possible ranks of tensor blow-ups of linear subspaces of matrices. It was proved by Ivanyos, Qiao and Subrahmanyam when the underlying field is sufficiently large. We show that if the field size is too small, the regularity lemma is false.
Keywords
Cite
@article{arxiv.1812.02223,
title = {The regularity lemma is false over small fields},
author = {Harm Derksen and Visu Makam},
journal= {arXiv preprint arXiv:1812.02223},
year = {2018}
}