13 problems

Let $p$ be a prime, let $(\mathcal{K},\mathcal{O},k)$ be a complete $p$-modular system with algebraically closed residue field $k$ of characteristic $p$, and let $G$ be a finite gr…

Let $\mathcal{O}$ be an arbitrary complete discrete valuation ring, let $G$ be a finite group, and let $b$ be a block idempotent of $G$ over $\mathcal{O}$ with an abelian defect gr…

Let $k$ be an algebraically closed field. Consider $k$-linear $\operatorname{Ext}$-finite hereditary categories satisfying Serre duality, and regard two such categories as equivale…

Let $A$ be a basic algebra, and suppose that $A$ is derived equivalent to a biserial fractional Brauer graph algebra (FBGA). Conjecture 1.3. Then $A$ is also a biserial FBGA. Since…

Let $A$ be a graded gentle or skew-gentle algebra, and let $\mathbf S=(S,\Sigma,\eta)$ be the graded surface associated to $A$. For a formal dissection $\Delta$ of $\mathbf S$, let…

Let $k$ be an algebraically closed field, and let twisted abelian varieties mean abelian varieties equipped with twists of their derived categories. For ordinary abelian varieties,…

Let $B^{\eta,\rho,d}_{R_p}$ and $B^{\eta,\rho',d'}_{R_p}$ be arbitrary spin blocks of symmetric groups, or let $(B^{\eta,\rho,d}_{R_p})_{0}$ and $(B^{\eta,\rho',d'}_{R_p})_{0}$ be…

Let $X$ and $Y$ be separated schemes of finite type over a field $k$, and suppose there is an equivalence $\mathrm{Perf}(X)\cong\mathrm{Perf}(Y)$. Dimension invariance conjecture.…

Let $F$ be an algebraically closed field of characteristic $p>0$, let $G$ be a finite group, and let $B$ be a block of $FG$ with defect group $D$ and fusion system…

Skowroński's conjecture. The class of weighted generalized triangulation algebras is closed under mutations and exhausts all algebras derived equivalent to weighted triangulation a…

Let $\mathcal{X}_{1,3}$ and $\mathcal{X}_{3,1}$ denote the Calabi-Yau threefolds studied by Donagi, Gao, and Schulz, whose Betti cohomology has torsion at primes $p$ dividing that…

Let $A$ be a piecewise hereditary algebra of tree type, let $\hat{A}$ be its repetitive category, and let $\phi$ be an automorphism of $\hat{A}$ with nonzero jump $n$. Write … for…

Cabanes–Rickard conjecture. This derived equivalence should in fact be a homotopy equivalence.