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This is a Quantitative Study study.

October 9, 2025Open Access

Galois groups of simple abelian varieties over finite fields and exceptional Tate classes

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New cases of the Tate conjecture were proved for abelian varieties over finite fields, indicating broader applicability.
The method relies on a combinatorial condition that describes exceptional classes tied to Galois groups and Newton polygons.
An algorithm was developed to determine the existence of particular abelian varieties from their Newton polygons and CM fields.
Ordinary geometrically simple varieties of prime dimension were shown to have maximal angle rank, refining previous findings.

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Implication

This research extends the Tate conjecture for abelian varieties over finite fields, indicating new results regarding exceptional classes and angle ranks.

Cite This Study

Arango-Piñeros et al. (2025) studied this question.

synapsesocial.com/papers/68e8439a9989581a2fd4e0b3 https://doi.org/10.48550/arxiv.2505.09589

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Implication

This research extends the Tate conjecture for abelian varieties over finite fields, indicating new results regarding exceptional classes and angle ranks.

Galois groups of simple abelian varieties over finite fields and exceptional Tate classes

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Discussion

Implication

Cite This Study

Galois groups of simple abelian varieties over finite fields and exceptional Tate classes

Key Points

Discussion

Implication

Cite This Study

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