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arXiv · 1211.4286

Elliptic minuscule pairs and splitting abelian varieties

V. Kumar Murty·Ying Zong
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Abstract

We partially answer, in terms of monodromy, Murty and Patankar's question: Given an absolutely simple abelian variety over a number field, does it have simple specializations at a set of places of positive Dirichlet density? The answer is based on the classification of pairs (G,V) consisting of a semi-simple algebraic group G over a non-archimedean local field and an absolutely irreducible representation V of G such that G admits a maximal torus acting irreducibly on V.

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V. Kumar Murty, Ying Zong. 2012-11-19. Elliptic minuscule pairs and splitting abelian varieties. https://arxiv.org/abs/1211.4286

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