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Mathematics > Number Theory

Title: On some abelian varieties of type IV

Authors: Steve Thakur
Abstract: We study a certain class of simple abelian varieties of type IV (in Albert's classification) over number fields with Mumford-Tate groups of type A. In particular, we show that such abelian varieties have ordinary reduction away from a set of places of Dirichlet density zero. We also study the splitting types and Newton polygons of the reductions of the abelian varieties of this type with small dimension (nine).
Subjects: Number Theory (math.NT)
Cite as: arXiv:1803.05954 [math.NT]
  (or arXiv:1803.05954v1 [math.NT] for this version)

Submission history

From: Steve Thakur [view email]
[v1] Thu, 15 Mar 2018 19:09:11 GMT (22kb)