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PreprintCC BY-NC-ND 4.0HAL

SUPERSINGULAR TATE CONJECTURE FOR IRREDUCIBLE SYMPLECTIC VARIETIES OF KNOWN TYPES: I

  • Lie Fu
  • Xuanlin Huang
  • Zhiyuan Li
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Abstract

We prove that for a supersingular irreducible symplectic variety admitting suitable lifting to characteristic zero has Tate Chow motive if it is of deformation type K3 [n] , OG6 (with Artin invariant ̸ = 4), or OG10 (with Artin invariant ̸ = 12), and has supersingular abelian Chow motive if it is of Kum n -type (with Artin invariant ̸ = 3). In particular, any product of those irreducible symplectic varieties satisfies the supersingular Tate conjecture for the whole ℓ-adic or crystalline cohomology ring.

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Cite

BibTeXRIS
BibTeX
@misc{fu2026supersingular,
  title = {{SUPERSINGULAR TATE CONJECTURE FOR IRREDUCIBLE SYMPLECTIC VARIETIES OF KNOWN TYPES: I}},
  author = {Lie Fu and Xuanlin Huang and Zhiyuan Li},
  howpublished = {HAL},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.38801},
  eprint = {2609.38801},
  archivePrefix = {arXiv},
  url = {https://hal.science/hal-05783404v1},
  note = {CC BY-NC-ND 4.0},
}
RIS
TY  - UNPB
TI  - SUPERSINGULAR TATE CONJECTURE FOR IRREDUCIBLE SYMPLECTIC VARIETIES OF KNOWN TYPES: I
AU  - Lie Fu
AU  - Xuanlin Huang
AU  - Zhiyuan Li
PY  - 2026
DA  - 2026/09/30
PB  - HAL
DO  - 10.48550/arxiv.2609.38801
UR  - https://hal.science/hal-05783404v1
AB  - We prove that for a supersingular irreducible symplectic variety admitting suitable lifting to characteristic zero has Tate Chow motive if it is of deformation type K3 [n] , OG6 (with Artin invariant ̸ = 4), or OG10 (with Artin invariant ̸ = 12), and has supersingular abelian Chow motive if it is of Kum n -type (with Artin invariant ̸ = 3). In particular, any product of those irreducible symplectic varieties satisfies the supersingular Tate conjecture for the whole ℓ-adic or crystalline cohomology ring.
ER  -