Cuspidal representations in the l-adic cohomology of the Rapoport-Zink space for GSp(4)

Details Cuspidal representations in the l-adic cohomology of the Rapoport-Zink space for GSp(4) Cuspidal representations in the l-adic cohomology of the Rapoport-Zink space for GSp(4)

2010-05-31

arxiv.org/abs/1005.5619v2

Mathematics

Representation Theory

31 pages, Minor modifications

Scientific paper

In this paper, we study the l-adic cohomology of the Rapoport-Zink tower for
GSp(4). We prove that the smooth representation of GSp_4(Q_p) 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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