For infinite-level EL Rapoport-Zink diamonds, the structure morphism is cohomologically smooth over the non-very-special locus, and a general geometric criterion for that locus is established, with the smoothness conjecture proved in the EL case.
Espaces de Banach-Colmez et faisceaux coh´ erents sur la courbe de Fargues- Fontaine
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A cohomological smoothness conjecture for moduli of mixed characteristic local shtukas with one leg
For infinite-level EL Rapoport-Zink diamonds, the structure morphism is cohomologically smooth over the non-very-special locus, and a general geometric criterion for that locus is established, with the smoothness conjecture proved in the EL case.