Auslander Conjecture in Homological Algebra

### Auslander Conjecture (disproved)
Let $A$ be an Artin algebra over a commutative Artinian ring $R$.
For any finitely generated left $A$-module $X$ there is a number $n_X ≥ 0$
such that for any finitely generated left $A$-module $Y$ satisfying $Ext^i(X,Y) = 0$ for $i ≫ 0$
it follows that $Ext^i(X,Y) = 0$ for any $i ≥ n_X$.

In particular, the bound $n_X$ may depend on $X$, but shall work for all $Y$ which have eventual $Ext$-vanishing with respect to $X$.

The conjecture was attributed to Maurice Auslander. The formulation above is taken from the arXiv article:
[D.A. Jorgensen and L.M. Şega, Nonvanishing cohomology and classes of Gorenstein rings](https://arxiv.org/abs/math/0306001)
published in [Adv. Math. 188 (2004), 470-490](https://doi.org/10.1016/j.aim.2003.11.003).
In this article, Jorgensen and Şega provide counterexamples to the Auslander conjecture.

Remark: Unfortunately, the naming may cause confusion with the [Auslander Conjecture of Louis Auslander](https://www.math.u-szeged.hu/~odor/auslander.htm) on affine crystallographic groups.

### Prerequisites needed
None.

### [AMS categories](https://github.com/google-deepmind/formal-conjectures/labels?q=ams-)

* ams-16 and ams-18 (Associative rings and algebras + Category theory; homological algebra)

### Choose either option
- [x] I plan on adding this conjecture to the repository
- [ ] This issue is up for grabs: I would like to see this conjecture added by somebody else