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Number Theory Seminar

Thursday, April 27, 2023
4:00pm to 5:00pm
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Linde Hall 387
Abelian covers of P^1 of p-ordinary Ekedahl-Oort type
Yuxin Lin, Department of Mathematics, Caltech,

Given a family of abelian covers of P1 and a prime p of good reduction, by considering the associated Deligne–Mostow Shimura variety, we obtain new lower bounds for the Ekedahl-Oort type, and the Newton polygon, at p of the curves in the family. In this paper, we investigate whether such lower bounds are sharp. In particular, we prove sharpeness when the number of branching points is at most five and p sufficiently large. Our result is a generalization of the result by Bouw, which proves the analogous statement for the p-rank, and it relies on the notion of Hasse-Witt triple introduced by Moonen.

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