Auslander–Reiten conjecture
Do vanishing higher extension groups force a module to be projective?
Algebras and modules
Representations, extensions and resolutions that reveal algebraic structure.
Subjects: Algebras and modules
Problems in this collection
4 problemsFinitistic dimension conjecture
For each finite-dimensional algebra, are finite projective dimensions of finitely generated modules bounded?
Alperin weight conjecture
Can each block’s irreducible representations in prime characteristic be counted entirely from local subgroup data?
Broué’s abelian defect group conjecture
Does an abelian-defect representation block retain its derived structure when replaced by its local normalizer block?