A counterexample to the $\phi$-dimension conjecture
Representation Theory
2022-08-25 v2 Rings and Algebras
Abstract
In 2005, the second author and Todorov introduced an upper bound on the finitistic dimension of an Artin algebra, now known as the {\phi}-dimension. The {\phi}-dimension conjecture states that this upper bound is always finite, a fact that would imply the finitistic dimension conjecture. In this paper, we present a counterexample to the {\phi}-dimension conjecture and explain where it comes from. We also discuss implications for further research and the finitistic dimension conjecture.
Cite
@article{arxiv.1911.00614,
title = {A counterexample to the $\phi$-dimension conjecture},
author = {Eric J. Hanson and Kiyoshi Igusa},
journal= {arXiv preprint arXiv:1911.00614},
year = {2022}
}
Comments
final version