2 problems

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The reductive local structure conjecture for algebraic stacks
Reductive local structure conjecture. Under these hypotheses, such an étale morphism exists.
Conjectureopenalgebraic-stacks local-structure positive-characteristicarXiv posted 2 days ago
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Benjamini–Georgakopoulos conjecture on local indistinguishability of Cayley graphs
Benjamini–Georgakopoulos conjecture. There exists $r\in\mathbb{N}$ such that, whenever a graph $G$ is $r$ -locally $F$ , $F$ covers $G$ .
Conjecturerefutedcayley-graphs graph-theory local-structurearXiv posted 2 days ago

The reductive local structure conjecture for algebraic stacks