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math.NT2025
Isogeny graphs of abelian varieties and singular ideals in orders
Sarah Arpin, Stefano Marseglia, Caleb Springer
Famously, Kohel proved that isogeny graphs of ordinary elliptic curves are beautifully structured objects, now called volcanos. We prove graph structural theorems for abelian varie…
math.NT2025
Weil polynomials of small degree
Stefano Marseglia
Honda and Tate showed that the isogeny classes of abelian varieties of dimension over a finite field are classified in terms of -Weil polynomials of degree $2…
math.NT2025
Labeling abelian varieties over finite fields
Edgar Costa, Taylor Dupuy, Stefano Marseglia +2
We describe a deterministic process to associate a practical, permanent label to isomorphism classes of abelian varieties defined over finite fields with commutative endomorphism a…