On some abelian varieties of type IV

Steve Thakur

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arXiv · 1803.05954

On some abelian varieties of type IV

Steve Thakur

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Abstract

We study a certain class of simple abelian varieties of type $\mathrm{IV}$ (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, thus confirming a special case of a broader conjecture of Serre's. We also study the splitting types and Newton polygons of the reductions of the abelian varieties of this type with small dimension (nine).

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Steve Thakur. 2018-03-15. On some abelian varieties of type IV. https://arxiv.org/abs/1803.05954

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