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

翻译：本文提出了一种新算法，通过关联的晶体上同调计算有限Drinfeld模任意自同态的特征多项式。我们的方法借鉴了Kedlaya利用Monsky-Washnitzer上同调计算超椭圆曲线上Frobenius自同态特征多项式的p-adic算法。针对Frobenius自同态的特殊情形，该方法采用小步大步算法进行优化，并在此情形下给出了复杂度分析，表明其相较于现有方法具有渐近优势。