Abstract
The group \(GL(r, {\mathbb{A}}_{f})\) acts (by Prop.4.15) on the moduli scheme \({M}_{r} = Spec{A}_{r} =\mathop{ \lim }_\longleftarrow {M}_{r,I}\) constructed in Theorem 4.10. The central group F × acts trivially. In this section we construct a covering scheme \({\widetilde{M}}_{r}\) of M r for which the action of \(GL(r, {\mathbb{A}}_{f})\) extends nontrivially to an action of \((GL(r, {\mathbb{A}}_{f}) \times{D}_{\infty }^{\times })/{F}^{\times }\), where D ∞ is a division algebra of rank r over F ∞ .
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Flicker, Y.Z. (2013). Covering Schemes. In: Drinfeld Moduli Schemes and Automorphic Forms. SpringerBriefs in Mathematics. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-5888-3_5
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