Compactifying Moduli Spaces for Abelian Varieties

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Arithmetic Compactifications of PEL-Type Shimura Varieties (2013, background): “Finally, we would like to mention that we are not working along the lines of the canonical compactifications constructed by Alexeev and Nakamura [1], or by Olsson [98], because it is not plausible that one could define general Hecke actions on their canonical compactifications.”
Logarithmic Geometry and Moduli (2010, background): “In [52], he isolates the normalization of the main component of V.”
Equidistribution in Families of Abelian Varieties and Uniformity (2021, unknown): “This follows, for example, by combining [68, Lemma 2.1.9], [ 61, Corollary of Theorem 1] and [63, Proposition 1].”