10 problems

Let $\mathfrak{O}$ be the coefficient ring and let $A$ be a finite-dimensional $\mathfrak{O}$-algebra. Write $\zeta_A(t)$ and $\zeta^{\lhd}_A(t)$ for its subalgebra and ideal zeta…

Let $\Lambda$ be a finite representation type algebra, and let $\widetilde{\mathcal{U}}_\Lambda$ and $\widetilde{\mathcal{M}}_\Lambda$ be the affine varieties associated with…

Let $A$ be a connected $\mathbb{R}$-algebra. An algebra is locally complexified-gentle of uniform type if it is Morita equivalent to an algebra satisfying condition (1) or (2) of T…

Rickard's conjecture. Any derived equivalence between flat algebras is standard.

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…

Derived dimension conjecture. The derived dimension of $A$ satisfies

Bridge-free matroid criterion. The algebras $\mathcal C_{G_1}^T$ and $\mathcal C_{G_2}^T$ are isomorphic if and only if their bridge-free matroids are isomorphic.

Let $\cA$ be a non-associative $\fo$-algebra that is free of rank $d$ as an $\fo$-module, where $\fo$ is the ring of integers in a number field $k$. Root-location conjecture. If…

Let $\cA$ be a non-associative $\fo$-algebra that is free of rank $d$ as an $\fo$-module, where $\fo$ is the ring of integers in a number field $k$. Zero-pole conjecture. The topol…

Let $\cA$ be a non-associative $\fo$-algebra that is free of rank $d$ as an $\fo$-module, where $\fo$ is the ring of integers in a number field $k$. Degree conjecture. … This is pr…