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Existence Theorem

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Abstract

In the proof of Theorem 10.8 we use the Grothendieck fixed-point formula of Theorem 6.6, which applies to the cohomology \({H}_{c}^{i}({\overline{X}}_{v}, \mathbb{L}(\rho ))\) of the geometric fiber \({\overline{X}}_{v} = {X}_{v} {\otimes }_{{\mathbb{F}}_{v}}{\overline{\mathbb{F}}}_{v}\) of the special fiber \({X}_{v} = {M}_{r,I} {\otimes }_{A}{\mathbb{F}}_{v}\) (of the moduli scheme M r, I ), which is a separated scheme of finite type over \({\mathbb{F}}_{v}\). This formula applies only to powers of the (geometric) Frobenius endomorphism Fr v ×1, and the conclusion of Theorem 10.8 concerns only the (Hecke) eigenvalues of the action of the Hecke algebra \({\mathbb{H}}_{v}\) of U v -biinvariant functions on G v , on this cohomology; as usual we put U v for GL(r, A v ).

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  1. Department of Mathematics, The Ohio State University, Columbus, OH, USA

    Yuval Z. Flicker

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Flicker, Y.Z. (2013). Existence Theorem. In: Drinfeld Moduli Schemes and Automorphic Forms. SpringerBriefs in Mathematics. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-5888-3_11

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