2 problems

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The exceptional canonical module conjecture for piecewise hereditary incidence algebras
Let $K\Delta$ be a PHI algebra derived equivalent to the category of coherent sheaves on a weighted projective line, and let $M$ be its canonical sincere $K\Delta$ -module. Here, a…
Conjectureopenexceptional-objects incidence-algebras piecewise-hereditary-algebrasarXiv posted 2 days ago
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Autoequivalence conjecture for exceptional objects on the Hirzebruch surface $\mathbb{F}_2$
Autoequivalence conjecture. For any exceptional object $\mathcal{E}\in D(\mathbb{F}_2)$ , there exists an autoequivalence $\Phi\in\operatorname{Auteq}(D(\mathbb{F}_2))$ such that…
Conjectureopenderived-categories exceptional-objects hirzebruch-surfacesarXiv posted 2 days ago

The exceptional canonical module conjecture for piecewise hereditary incidence algebras