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Cuspidal representations in the l-adic cohomology of some Rapoport-Zink spaces

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Rapoport-Zink spaces are certain moduli spaces of quasi-isogenies of p-divisible groups with additional structures, and can be regarded as local analogues of Shimura varieties. In this talk, we will consider the l-adic cohomology of two Rapoport-Zink spaces; one is the Lubin-Tate space (the Rapoport-Zink space for GL(n)) and the other is the Rapoport-Zink space for GSp(4). I will explain the following non-cuspidality results on these cohomology groups: for GL(n), cuspidal representation appears only in the cohomology of degree n-1, and for GSp(4), it appears only in the cohomology of degree 2, 3 and 4. The proof is purely local and does not require global automorphic methods.

This talk is part of the Number Theory Seminar series.

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