We give a formula for the essential dimensions of isogenies A→ A' of complex abelian varieties when the degree of the isogeny is coprime to ( A)!. As a corollary, we show that the p-multiplication map (where p is a prime) on an abelian variety is incompressible when p> A or when A≤ 4. This confirms a conjecture of Brosnan for most primes.
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Ziquan Zhuang (2024) studied this question.
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