5 problems

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A variant of the rational HK conjecture for ample groupoids
Variant of the HK conjecture. One should have
Conjecturesolvedetale-groupoids homology k-theoryarXiv posted 2 days ago
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Hurewicz-type conjecture for dynamic asymptotic dimension of groupoid homomorphisms
Hurewicz-type conjecture. For every continuous groupoid homomorphism $\pi:G\rightarrow H$ ,
Conjectureopendynamic-asymptotic-dimension etale-groupoids groupoid-homomorphismsarXiv posted 2 days ago
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Matui's AH conjecture for minimal Cantor groupoids
AH conjecture. There exists an exact sequence
Conjectureopenetale-groupoids full-groups groupoid-homologyarXiv posted 2 days ago
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The AH conjecture for topological full groups of minimal étale groupoids
AH conjecture. There exists an exact sequence
Conjectureopenetale-groupoids groupoid-homology topological-full-groupsarXiv posted 2 days ago
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The HK conjecture for minimal étale groupoids
HK conjecture. The even and odd homology groups of $\mathcal{G}$ satisfy
Conjectureopenetale-groupoids groupoid-homology operator-algebrasarXiv posted 2 days ago

A variant of the rational HK conjecture for ample groupoids