Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
8904877 | Advances in Mathematics | 2018 | 18 Pages |
Abstract
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.
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Physical Sciences and Engineering
Mathematics
Mathematics (General)
Authors
Dan Abramovich, Anthony Várilly-Alvarado,