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arXiv · 1905.04086

The Mumford-Tate conjecture implies the algebraic Sato-Tate conjecture of Banaszak and Kedlaya

Victoria Cantoral Farfán·Johan Commelin
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Abstract

The algebraic Sato-Tate conjecture was initially introduced by Serre and then discussed by Banaszak and Kedlaya. This note shows that the Mumford-Tate conjecture for an abelian variety A implies the algebraic Sato-Tate conjecture for A. The relevance of this result lies mainly in the fact that the list of known cases of the Mumford-Tate conjecture was up to now a lot longer than the list of known cases of the algebraic Sato-Tate conjecture.

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Victoria Cantoral Farfán, Johan Commelin. 2019-05-10. The Mumford-Tate conjecture implies the algebraic Sato-Tate conjecture of Banaszak and Kedlaya. https://arxiv.org/abs/1905.04086

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