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Tower of coverings and polylog-size coverings of rational points

  • Kenneth Chung Tak Chiu
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Abstract

We prove that a smooth irreducible proper variety over a number field admits polylogarithmic-size coverings of rational points of bounded height if it admits a tower of finite étale coverings satisfying several conditions. One of the conditions is a height comparison on twists of the finite étale covers. We prove that these conditions hold for abelian varieties.

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Cite

BibTeXRIS
BibTeX
@misc{chiu2026tower,
  title = {{Tower of coverings and polylog-size coverings of rational points}},
  author = {Kenneth Chung Tak Chiu},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.06166},
  eprint = {2610.06166},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.06166},
}
RIS
TY  - UNPB
TI  - Tower of coverings and polylog-size coverings of rational points
AU  - Kenneth Chung Tak Chiu
PY  - 2026
DA  - 2026/10/05
PB  - arXiv
DO  - 10.48550/arxiv.2610.06166
UR  - https://arxiv.org/abs/2610.06166
AB  - We prove that a smooth irreducible proper variety over a number field admits polylogarithmic-size coverings of rational points of bounded height if it admits a tower of finite étale coverings satisfying several conditions. One of the conditions is a height comparison on twists of the finite étale covers. We prove that these conditions hold for abelian varieties.
ER  -