Etale cohomology of diamonds
By Peter Scholze. 2017
184 citations recorded by the source corpus.
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 $\mathbb Z_p$ 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.
Subfields: Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/c5c69849aaf43e3242d7aeebce2342c98dfce04c
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In Geometry and Topology
- B. Bhatt
- Peter Scholze
- Ruochuan Liu
- Kiran S. Kedlaya
- Wiesława Nizioł
- A. Mathew
- A. Beilinson
- Laurent Fargues
In Mathematical Physics
- B. Bhatt
- Peter Scholze
- Ruochuan Liu
- Kiran S. Kedlaya
- Wiesława Nizioł
- A. Beilinson
- A. Mathew
- Laurent Fargues
Citations in the corpus
- Prismatic $F$-crystals and crystalline Galois representations (2021, methodology): “We will use that the association X 7→ D lisse(Xη,Zp) defines a sheaf of ∞-categories for the quasisyntomic topology on X , as follows from the v-descent results in [Sch17] (and the observation that any quasisyntomic cover of X induces a v-cover of Xη).”