Research profile

Peter Scholze

Works on geometrization.

NP-RC-034285

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Geometrization

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Their work in this field since 2016, with the older papers the site recommends. Titles open each paper's page, with its abstract, PDF and HTML versions; Connections shows the papers closest to it. The arXiv listing has the complete record.

2017

math.AGv4arXiv:1709.07343

Etale cohomology of diamonds

Peter Scholze

Motivated by problems on the étale 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 étale cohomology of diamonds, and more generally small v-stacks on the category of perfectoid spaces of characteristic . Using a natural functor from analytic adic spaces over to diamonds which identifies étale sites, this induces a similar formalism in that setting, which in the noetherian setting recovers the formalism from Huber's book.

Geometrization
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