Geodesic
The pro-étale cohomology of Drinfeld's upper half space
Documenta mathematica, Tome 26 (2021), pp. 1395-1421.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

We determine the geometric pro-étale cohomology of Drinfeld's upper half space over a $p$-adic field $K$. The strategy is different from the one given by [\textit{P. Colmez} et al., Invent. Math. 219, No. 3, 873--985 (2020; Zbl 1475.11110)] and is based on the approach developed in [\textit{S. Orlik}, Invent. Math. 172, No. 3, 585--656 (2008; Zbl 1136.22009)] describing global sections of equivariant vector bundles.
Classification : 14F20, 14G20, 11F85, 14F30, 22E50
Keywords: pro-étale cohomology, Drinfeld half space 
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     author = {Orlik, Sascha},
     title = {The pro-\'etale cohomology of {Drinfeld's} upper half space},
     journal = {Documenta mathematica},
     pages = {1395--1421},
     publisher = {mathdoc},
     volume = {26},
     year = {2021},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DOCMA_2021__26__a20/}
}
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Orlik, Sascha. The pro-étale cohomology of Drinfeld's upper half space. Documenta mathematica, Tome 26 (2021), pp. 1395-1421. http://geodesic.mathdoc.fr/item/DOCMA_2021__26__a20/