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We study the geometry and the cohomology of the tamely ramified cover of Drinfeld’s p-adic symmetric space over a p-adic field K. For this tame level, we prove, in a purely local way, most of a conjecture of Harris on the form of the $$\ell $$ ℓ -adic cohomologies, as well as the torsion freeness of the integral cohomology. In this paper, we also compute the $$\ell $$ ℓ -adic cohomology...
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