The stabilization of the Frobenius-Hecke traces on the intersection cohomology of orthogonal Shimura varieties
AbstractThe orthogonal Shimura varieties are associated to special orthogonal groups over Q of signature (n, 2) at infinity. In this work we prove a version of Morel’s formula for the Frobenius-Hecke traces on the intersection cohomology of their Baily-Borel compactifications. We then stabilize the formula, in terms of Kottwitz’s simplified expression for the geometric side of the Arthur-Selberg trace formula for test functions that are stable cuspidal at infinity.
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