Abstract
Motivated by problems on the etale cohomology of Rapoport–Zink spaces and their generalizations, as well as Fargues’s geometrization conjecture for the local Langlands correspondence, we develop a six functor formalism for the etale cohomology of diamonds, and more generally small v-stacks on the category of perfectoid spaces of characteristic p. Using a natural functor from analytic adic spaces over Zp to diamonds which identifies etale sites, this induces a similar formalism in that setting, which in the noetherian setting recovers the formalism from Huber’s book.
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