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SUMMARY:Cuspidal representations in the l-adic cohomology of some Rapoport
 -Zink spaces - Yoichi Mieda (Kyushu University)
DTSTART:20101026T133000Z
DTEND:20101026T143000Z
UID:TALK26361@talks.cam.ac.uk
CONTACT:Tom Fisher
DESCRIPTION:Rapoport-Zink spaces are certain moduli spaces of quasi-isogen
 ies of\np-divisible groups\nwith additional structures\, and can be regard
 ed as local analogues of\nShimura varieties.\nIn this talk\, we will consi
 der the l-adic cohomology of two Rapoport-Zink\nspaces\;\none is the Lubin
 -Tate space (the Rapoport-Zink space for GL(n)) and the\nother \nis the Ra
 poport-Zink space for GSp(4). \nI will explain the following non-cuspidali
 ty results on these cohomology\ngroups:\nfor GL(n)\, cuspidal representati
 on appears only in the cohomology of degree\nn-1\,\nand for GSp(4)\, it ap
 pears only in the cohomology of degree 2\, 3 and 4.\nThe proof is purely l
 ocal and does not require global automorphic methods.\n
LOCATION:MR13
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