The Frobenius-Hecke trace on the cohomology of two-slope Newton strata of compact unitary Kottwitz varieties is expressed as an explicit finite sum over type I and type II automorphic representations.
An automorphic description of the zeta function of the basic stratum of certain Kottwitz varieties
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abstract
We derive formulas for the number of points on the basic stratum of certain Kottwitz varieties in terms of automorphic representations and certain explicit polynomials, for which we present efficient algorithms for computation. We obtain our results using the trace formula, base change, representations of general linear groups over p-adic fields, and a truncation of the formula of Kottwitz for the number of points on Shimura varieties over finite fields.
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The cohomology of certain intermediate strata of Kottwitz varieties
The Frobenius-Hecke trace on the cohomology of two-slope Newton strata of compact unitary Kottwitz varieties is expressed as an explicit finite sum over type I and type II automorphic representations.