Difference between revisions of "Open problems"
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Revision as of 12:41, 26 August 2018
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 [math]{\rm Pic}_\mathcal{O}(B)[/math] always finite?
- Is every Morita equivalence between [math]\mathcal{O}[/math]-blocks endopermutation source?
Open cases for classifications of Morita equivalence classes for a given [math]p[/math]-group
- Which Brauer trees give rise to blocks with defect group [math]C_7[/math]? (This is the smallest cyclic group for which the classification is not known).
Picard groups
- What is [math]{\rm Pic}_\mathcal{O}(B_0(\mathcal{O} J_1))[/math]?
