Abstract
We compute the integral p-adic étale cohomology of Drinfeld symmetric spaces of any dimension. This refines the computation of the rational p-adic étale cohomology from our recent work on Stein spaces. The main tools are: the computation of the integral de Rham cohomology from that work and, as a new tool, the integral p-adic comparison theorems of Bhatt–Morrow–Scholze and Česnavičius–Koshikawa which replace the quasi-integral comparison theorem of Tsuji. Along the way, we compute the -cohomology of Drinfeld symmetric spaces.
Acknowledgments
The third author would like to thank the Mathematical Sciences Research Institute at Berkeley for their hospitality during the 2019 spring semester when parts of this paper were written. We would like to thank Bhargav Bhatt for suggesting that derived completions could simplify our original proof (which they did!). We thank Kęstutis Česnavičius and Matthew Morrow for helpful discussions related to the subject of this paper. Last but not least, we thank the referees for a very careful reading of the paper and many corrections/suggestions that we have incorporated into the final exposition.
This work was partially supported by Agence Nationale de la Recherche project ANR-14-CE25 and by National Science Foundation grant DMS-1440140.
Citation
Pierre Colmez. Gabriel Dospinescu. Wiesława Nizioł. "Integral p-adic étale cohomology of Drinfeld symmetric spaces." Duke Math. J. 170 (3) 575 - 613, 15 February 2021. https://doi.org/10.1215/00127094-2020-0084
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