On the l-adic cohomology of some p-adically uniformized Shimura varieties
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🧮 math.NT
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cohomologyshimuravarietiesadicsomeadicallyadmitcases
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We determine the Galois representations inside the $l$-adic cohomology of some unitary Shimura varieties at split places where they admit uniformization by finite products of Drinfeld upper half spaces. Our main results confirm Langlands-Kottwitz's description of the cohomology of Shimura varieties in new cases.
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