INTEGRAL STRUCTURES IN THE p-ADIC HOLOMORPHIC DISCRETE SERIES
نویسنده
چکیده
For a local non-Archimedean field K we construct GLd+1(K)equivariant coherent sheaves VOK on the formal OK -scheme X underlying the symmetric space X over K of dimension d. These VOK are OK -lattices in (the sheaf version of) the holomorphic discrete series representations (in Kvector spaces) of GLd+1(K) as defined by P. Schneider. We prove that the cohomology H(X,VOK ) vanishes for t > 0, for VOK in a certain subclass. The proof is related to the other main topic of this paper: over a finite field k, the study of the cohomology of vector bundles on the natural normal crossings compactification Y of the Deligne-Lusztig variety Y 0 for GLd+1/k (so Y 0 is the open subscheme of Pk obtained by deleting all its k-rational hyperplanes).
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