Labeling abelian varieties over finite fields

2025/01/28 by Costa, Edgar, Dupuy, Taylor, Marseglia, Stefano +2
#11C20 #11R54 #11Y40 #13H10 #14H20 #14K15 #15B36 #16H10 #16H20 #Algebraic Geometry (math.AG) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2501.17012

Abstract

We describe a deterministic process to associate a practical, permanent label to isomorphism classes of abelian varieties defined over finite fields with commutative endomorphism algebra as long as they are ordinary or defined over a prime field. In the ordinary case, we also provide labels for the polarizations they admit.

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