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Asymptotics of local height pairing without Hodge conjecture

  • Yuta Nakayama
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Abstract

We remove the assumption of the Hodge conjecture from the asymptotic formula for the Archimedean local height established in our previous work. We also remove other minor assumptions. We achieve this by exploiting the cohomological nature of Beilinson's local intersection index rather than arguing motivically.

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Cite

BibTeXRIS
BibTeX
@misc{nakayama2026asymptotics,
  title = {{Asymptotics of local height pairing without Hodge conjecture}},
  author = {Yuta Nakayama},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.30574},
  eprint = {2610.30574},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.30574},
}
RIS
TY  - UNPB
TI  - Asymptotics of local height pairing without Hodge conjecture
AU  - Yuta Nakayama
PY  - 2026
DA  - 2026/10/22
PB  - arXiv
DO  - 10.48550/arxiv.2610.30574
UR  - https://arxiv.org/abs/2610.30574
AB  - We remove the assumption of the Hodge conjecture from the asymptotic formula for the Archimedean local height established in our previous work. We also remove other minor assumptions. We achieve this by exploiting the cohomological nature of Beilinson's local intersection index rather than arguing motivically.
ER  -