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Isogeny Classes

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Drinfeld Moduli Schemes and Automorphic Forms

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Abstract

The main tool which is applied in Part IV is a comparison of the “arithmetic” fixed point formula with the “analytic” trace formula. To carry out this comparison we need to describe the arithmetic data, which is the cardinality of the set of points on the fiber M r,v at v of the moduli scheme M r , over finite field extensions of \({\mathbb{F}}_{v} = A/v\), or, equivalently, the set \({M}_{r,v}({\overline{\mathbb{F}}}_{v})\) with the action of the Frobenius morphism on it, by group theoretic data which appears in the trace formula. In this Chapter we begin with a description (following Drinfeld [D) of the set of isogeny classes in \({M}_{r,v}({\overline{\mathbb{F}}}_{v})\) in terms of certain field extensions of F; these will be interpreted as tori of GL(r) in the trace formula.

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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). Isogeny Classes. In: Drinfeld Moduli Schemes and Automorphic Forms. SpringerBriefs in Mathematics. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-5888-3_7

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