# Open problems

This page is for open problems, large and small, relating to module categories for blocks. Missing data is also flagged within tables elsewhere on this site.

## General problems

• Is the isomorphism type of the defect group a Morita invariant?
• Is ${\rm Pic}_\mathcal{O}(B)$ always finite?
• Is every Morita equivalence between $\mathcal{O}$-blocks endopermutation source?

## Open cases for classifications of Morita equivalence classes for a given $p$-group

• Which Brauer trees give rise to blocks with defect group $C_7$? (This is the smallest cyclic group for which the classification is not known).

## Picard groups

• What is ${\rm Pic}_\mathcal{O}(B_0(\mathcal{O} J_1))$?