On the Cohomology of the Affine Space
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We compute the p-adic geometric pro-étale cohomology of the rigid analytic affine space (in any dimension). This cohomology is non-zero, contrary to the étale cohomology, and can be described by means of differential forms.
We would like to thank the referee for a careful reading of the manuscript and useful suggestions for improving the exposition.
- 2.P. Colmez, G. Dospinescu, W. NizioŁ, Cohomology of \(p\)-adic Stein spaces. Invent. Math. 219 (2020), 873–985.Google Scholar
- 3.P. Colmez, W. NiziołŁ, Syntomic complexes and \(p\)-adic nearby cycles, Invent. Math. 208 (2017), 1–108.Google Scholar
- 4.J.-M. Fontaine, W. Messing, \(p\)-adic periods and \(p\)-adic étale cohomology, Current Trends in Arithmetical Algebraic Geometry (K. Ribet, ed.), Contemporary Math., vol. 67, AMS, Providence, 1987, 179–207.Google Scholar