Rationality hypothesis for noetherian connected graded algebras with balanced dualizing complexes

Let $A$ be a noetherian connected graded algebra with a balanced dualizing complex. Hypothesis

is the assertion that every finitely generated graded \left and \right $A$-module is rational over $\mathbb{Q}$, meaning that its Hilbert series and the corresponding alternating local-cohomology series are rational functions over $\mathbb{Q}$ and agree as rational functions. **Rationality hypothesis.** Every noetherian connected graded algebra with balanced dualizing complex satisfies Hypothesis

. Rationality over $\mathbb{Q}$ is known for many classes of graded algebras, including PI algebras and factor rings of AS-regular algebras; the stated implication is presented here as a hypothesis and its resolution is not determined by the supplied text.