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arXiv · 1911.00614

A counterexample to the $\phi$-dimension conjecture

Eric J. Hanson·Kiyoshi Igusa
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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.

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BibTeXRIS

Eric J. Hanson, Kiyoshi Igusa. 2019-11-01. A counterexample to the $\phi$-dimension conjecture. https://doi.org/10.1007/s00209-021-02795-7

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