Cuspidal representations in the l-adic cohomology of the Rapoport-Zink space for GSp(4)
Abstract
In this paper, we study the l-adic cohomology of the Rapoport-Zink tower for GSp(4). We prove that the smooth representation of GSp4(Qp) obtained as the i-th compactly supported l-adic cohomology of the Rapoport-Zink tower has no quasi-cuspidal subquotient unless i=2,3,4. Our proof is purely local and does not require global automorphic methods.
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