2 problems

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Herschend–Iyama–Oppermann conjecture on nonzero regular modules
Herschend–Iyama–Oppermann conjecture. For every $n$ -representation infinite algebra, $\mathscr{R}$ is non-zero.
Conjectureopenhigher-representation-theory representation-infinite-algebrasarXiv posted 2 days ago
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Rouquier's conjecture on subcategories affording abelian 2-representations
Rouquier's conjecture. A subcategory affording an abelian $2$ -representation should exist.
Conjectureopen2-representations higher-representation-theoryarXiv posted 2 days ago

Herschend–Iyama–Oppermann conjecture on nonzero regular modules