English

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.

Keywords

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}
}

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final version

R2 v1 2026-06-23T12:02:45.516Z