Skip to content
DraconiticResearch
Search Sources API
197,768 studies31 sourcesUpdated 38 min ago
PreprintCC BY 4.0arXiv

Isogeny rigidity under algebraic group actions and finite translation orbits

  • Paolo Dolce
  • Francesco Tropeano
  • Ekaterina Amerik
Open at sourcePDFDOICite

Abstract

We study finite orbits generated by fibrewise translations on varieties carrying two abelian fibrations. Under natural dominance and generation hypotheses, non-isotriviality of the first family forces points with finite orbit to lie over proper closed subsets of both bases. This extends results of Corvaja, Tsimerman and Zannier to complex families of arbitrary, possibly different relative dimensions, including torsors. The proof combines relative Manin-Mumford with a general isogeny rigidity theorem for algebraic group actions.

Related

  1. Frobenius Alexander quandles, knot colorings, and isogeny classes of abelian varieties over finite fields
    WonTae Hwang
    arXivPreprintarXiv licenceFull textAlgebra & number theoryGeometry & topologyarXiv
  2. Directional measure rigidity for time-changed first row unipotent actions
    Davide Ravotti, Daren Wei
    arXivPreprintarXiv licenceFull textDynamical systemsarXiv
  3. IC-rigidity for abelian actions
    Adam Kanigowski, Kosma Kasprzak, Miriam Lorenzo-Laguno
    arXivPreprintarXiv licenceFull textDynamical systemsarXiv
  4. Rigidity of algebraic sets with small distortion
    Alexandre Fernandes, Edson Sampaio
    arXivPreprintarXiv licenceFull textAlgebra & number theoryarXiv
  5. Folded-Algebraic Matroids: Characteristic Rigidity and Almost-Entropic Separation
    Shahram Khazaei
    arXivPreprintCC BY 4.0Full textCombinatorics & discrete mathematicsarXiv

Cite

BibTeXRIS
BibTeX
@misc{dolce2026isogeny,
  title = {{Isogeny rigidity under algebraic group actions and finite translation orbits}},
  author = {Paolo Dolce and Francesco Tropeano and Ekaterina Amerik},
  howpublished = {arXiv},
  year = {2026},
  month = nov,
  doi = {10.48550/arxiv.2611.03606},
  eprint = {2611.03606},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2611.03606},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Isogeny rigidity under algebraic group actions and finite translation orbits
AU  - Paolo Dolce
AU  - Francesco Tropeano
AU  - Ekaterina Amerik
PY  - 2026
DA  - 2026/11/02
PB  - arXiv
DO  - 10.48550/arxiv.2611.03606
UR  - https://arxiv.org/abs/2611.03606
AB  - We study finite orbits generated by fibrewise translations on varieties carrying two abelian fibrations. Under natural dominance and generation hypotheses, non-isotriviality of the first family forces points with finite orbit to lie over proper closed subsets of both bases. This extends results of Corvaja, Tsimerman and Zannier to complex families of arbitrary, possibly different relative dimensions, including torsors. The proof combines relative Manin-Mumford with a general isogeny rigidity theorem for algebraic group actions.
ER  -