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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
The Spine of a Supersingular -Isogeny graph
Taha Hedayat, Sarah Arpin, Renate Scheidler
Supersingular elliptic curve -isogeny graphs over finite fields offer a setting for a number of quantum-resistant cryptographic protocols. The security analysis of these sche…
math.NT2025
Cycles and Cuts in Supersingular L-Isogeny Graphs
Sarah Arpin, Ross Bowden, James Clements +3
Supersingular elliptic curve isogeny graphs underlie isogeny-based cryptography. For isogenies of a single prime degree , their structure has been investigated graph-theoreti…