Computing the Characteristic Polynomial of Endomorphisms of a finite Drinfeld Module using Crystalline Cohomology

02/16/2023

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by   Yossef Musleh, et al.

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We present a new algorithm for computing the characteristic polynomial of an arbitrary endomorphism of a finite Drinfeld module using its associated crystalline cohomology. Our approach takes inspiration from Kedlaya's p-adic algorithm for computing the characteristic polynomial of the Frobenius endomorphism on a hyperelliptic curve using Monsky-Washnitzer cohomology. The method is specialized using a baby-step giant-step algorithm for the particular case of the Frobenius endomorphism, and in this case we include a complexity analysis that demonstrates asymptotic gains over previously existing approaches