16 problems

Let $R=k[x_1,\ldots,x_n]$, let ${\mathfrak c}\subset R$ be a general complete intersection of type $(d_1,\ldots,d_c)$, and let $A=R/I$ be relatively compressed with respect to…

Minimal-generator conjecture. If $d$ is odd, then $\operatorname{Ann}(H_{2d+1})$ has no minimal generators in degree $d+2$, and

Let $A=k[\![x,y]\!]/J$ be an AG $k$-algebra, let $I$ be an ideal in $A$, and let $H$ be a $2$-admissible $G(I)$-Gorenstein sequence. A symmetric decomposition is a decomposition of…

Let $A=k[ … /J$ be an AG $k$-algebra. Let $H=(h0,h1,\ldots,hu)$ be a $2$-admissible sequence, where a sequence is partially strict unimodal if…

Koszul Roller Coaster conjecture. There exists such an algebra satisfying

A noetherian Hopf algebra is a Hopf algebra satisfying the ascending chain condition on left and right ideals. Brown-Goodearl conjecture. Every noetherian Hopf algebra is Artin–Sch…

Let $S={\Bbbk}[x,y,z]$, let $d$ be a positive integer, and let $[S/I]\in\mathrm{Hilb}^d(\mathbb{A}^3)$ be a smoothable point. Broken Gorenstein characterization conjecture. The fol…

Additive-action multiplicity conjecture. There are at least two non-equivalent induced additive actions on $X$.

Iwanaga–Gorenstein Wakamatsu tilting conjecture. Any Wakamatsu tilting $\Lambda$-module is tilting.

Self-orthogonal module conjecture. Every self-orthogonal $\Lambda$-module has finite projective dimension.

Let $k$ be the base field, let $M\in M_3(k)$, and let $\mathcal{A}_{\mathcal{O}_{-1}(k^3)}(M)$ denote the associated cochain DG skew polynomial algebra. Write…

Let $A$ be an artinian standard graded algebra over a field $k$, and write its Hilbert function as $h=(1,h_1,\dots,h_e)$, where $e$ is the socle degree. A Hilbert function is Goren…

Gorenstein and palindromicity conjecture. If $\tau$ is trivial, then $M_c(S_n,\mathfrak{h},\tau)/J_c(S_n,\mathfrak{h},\tau)$ is Gorenstein for all $n$, both when $c\in\mathbf{F}_p$…

Let $R/I$ be an artinian Gorenstein algebra of codimension $r\geq 3$ and socle degree $e$, and assume that $h_2=r$. The $h_2=r$ conjecture. Then … Furthermore, if $e\geq 4$, the id…

Let $R/I$ be an artinian Gorenstein algebra presented by quadrics, with socle degree at least $3$, and suppose that $R$ is defined over a field of characteristic zero. The WLP conj…

Let $(1,h_1,\ldots,h_e)$ be a Gorenstein $h$-vector, so $h_e=1$ and the entries are symmetric. Fix an index $i$ and a positive integer $\alpha$. Suppose that both … and … are Goren…