Browsing by Author "Abramovich, Dan"

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    Level structures on Abelian varieties, Kodaira dimensions, and Lang's conjecture
    (Elsevier, 2018) Abramovich, Dan; Várilly-Alvarado, Anthony
    Assuming Lang's conjecture, we prove that for a prime p, number field K, and positive integer g, there is an integer r such that no principally polarized abelian variety A/K has full level-pr structure. To this end, we use a result of Zuo to prove that for each closed subvariety X in the moduli space Ag of principally polarized abelian varieties of dimension g, there exists a level mX such that the irreducible components of the preimage of X in Ag[m] are of general type for m>mX.