Mathematics, Algebraic Geometry, Algebraic Geometry (math.AG), Number Theory (math.NT)

journal:

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date:

2023-07-24 16:00:00

Abstract

We extend Moonen's definition of Ekedahl-Oort types of smooth curves and abelian varieties in terms of Hasse-Witt triples to all stable curves and semi-abelian varieties and show that it matches Ekedahl and van der Geer's definition of Ekedahl-Oort types of semi-abelian varieties. Using this intrinsic insight, we can compute the dimensions of certain Ekedahl-Oort loci of curves and generalize some previously known results about the dimensions of the $p$-rank and $a$-number loci of curves.