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

2023/02/16 by Yossef Musleh, Musleh, Yossef, Éric Schost +1 · 1 citation
Computer Science · Mathematics · #Algebraic Geometry and Number Theory #Commutative Algebra and Its Applications #FOS: Computer and information sciences #Symbolic Computation (cs.SC) #Topological and Geometric Data Analysis

paper · pdf · doi:10.48550/arxiv.2302.08611

openalex publication_date 2023/02/16 · openalex created_date 2023/02/22 · openalex updated_date 2026/07/28

Abstract

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

Cited by

• On the Characteristic Polynomial of Linearized Polynomials

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