6 problems

Cancellation conjecture.

A noetherian AS-regular algebra is a noetherian algebra satisfying the Artin–Schelter regularity conditions; a domain is a ring with no nonzero zero divisors. Domain conjecture. Ev…

An algebra $A$ is GK-Cohen–Macaulay if it satisfies the GK-Cohen–Macaulay property in the sense of the cited definition. GK-Cohen–Macaulay conjecture. Every AS regular algebra has…

Let $A$ be an AS regular algebra, and let $G$ be a finite group of graded automorphisms of $A$. A reflection of $A$ is an automorphism of the kind defined in the surrounding discus…

Let $S$ be an AS-regular algebra, and let $u$ be its Nakayama automorphism. The homological determinant conjecture. If $nu$ is the Nakayama automorphism of an AS-regular algeb…

Extension conjecture. A version of this lemma holds for general AS regular algebras generated in degree $1$. Such a result would extend the relationship between the Nakayama automo…