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The Tate conjecture for abelian fivefolds over finite fields

  • Ningyi Li
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Abstract

We prove the Tate conjecture for abelian fivefolds over finite fields. The proof constructs correspondences for a residual motive using a Moret--Bailly family, Gross--Schoen heights, and monodromy. We also prove standard conjecture~Dℓ over F̅p and independence of ℓ of rational cycle class kernels over algebraically closed fields of characteristic p. Over finite fields, rational and numerical equivalence agree with rational coefficients, and higher algebraic K-groups vanish rationally.

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Cite

BibTeXRIS
BibTeX
@misc{li2026tate,
  title = {{The Tate conjecture for abelian fivefolds over finite fields}},
  author = {Ningyi Li},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2609.06265},
  eprint = {2609.06265},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.06265},
}
RIS
TY  - UNPB
TI  - The Tate conjecture for abelian fivefolds over finite fields
AU  - Ningyi Li
PY  - 2026
DA  - 2026/10/08
PB  - arXiv
DO  - 10.48550/arxiv.2609.06265
UR  - https://arxiv.org/abs/2609.06265
AB  - We prove the Tate conjecture for abelian fivefolds over finite fields. The proof constructs correspondences for a residual motive using a Moret--Bailly family, Gross--Schoen heights, and monodromy. We also prove standard conjecture~D_ℓ over F̅_p and independence of ℓ of rational cycle class kernels over algebraically closed fields of characteristic p. Over finite fields, rational and numerical equivalence agree with rational coefficients, and higher algebraic K-groups vanish rationally.
ER  -