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Deligne’s congruence and supersingular reduction of Drinfeld modules

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Abstract.

Most rank two Drinfeld modules are known to have infinitely many supersingular primes. But how many supersingular primes of a given degree can a fixed Drinfeld module have? In this paper, a congruence between the Hasse invariant and a certain Eisenstein series is used for obtaining a bound on the number of such supersingular primes. Certain exceptional cases correspond to zeros of certain Eisenstein series with rational j-invariants.

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Authors and Affiliations

  1. Max-Planck-Institut für Mathematik, Gottfried-Claren-Straße 26, D-53225 Bonn, Germany , , , , , , DE

    Gunther Cornelissen

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  1. Gunther Cornelissen
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Received: 19.2.1998

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Cornelissen, G. Deligne’s congruence and supersingular reduction of Drinfeld modules. Arch. Math. 72, 346–353 (1999). https://doi.org/10.1007/s000130050342

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  • DOI: https://doi.org/10.1007/s000130050342

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