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PreprintCC BY-NC-ND 4.0arXiv

Wild automorphisms and compound isotriviality

  • Jason Bell
  • Rahim Moosa
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Abstract

Inspired by the model theory of difference fields in characteristic zero, a class of automorphisms of an algebraic variety, here called compound fundamental isotrivial, is introduced. These are algebraic dynamical systems that are built up via a finite sequence of equivariant fibrations from (possibly nonautonomous) algebraic dynamics which trivialise after base extension over themselves. Every wild automorphism of an abelian variety is compound fundamental isotrivial. Conversely, it is shown that the only irreducible projective varieties admitting a wild automorphism that is compound fundamental isotrivial are the abelian varieties. That is, the wild automorphism conjecture of Reichstein, Rogalski, and Zhang is here proven for compound fundamental isotrivial dynamics. Along the way, a counterexample to the naive generalisation of the conjecture to the nonautonomous setting of σ-varieties is provided.

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Cite

BibTeXRIS
BibTeX
@misc{bell2026wild,
  title = {{Wild automorphisms and compound isotriviality}},
  author = {Jason Bell and Rahim Moosa},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2606.20228},
  eprint = {2606.20228},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2606.20228},
  note = {CC BY-NC-ND 4.0},
}
RIS
TY  - UNPB
TI  - Wild automorphisms and compound isotriviality
AU  - Jason Bell
AU  - Rahim Moosa
PY  - 2026
DA  - 2026/09/15
PB  - arXiv
DO  - 10.48550/arxiv.2606.20228
UR  - https://arxiv.org/abs/2606.20228
AB  - Inspired by the model theory of difference fields in characteristic zero, a class of automorphisms of an algebraic variety, here called compound fundamental isotrivial, is introduced. These are algebraic dynamical systems that are built up via a finite sequence of equivariant fibrations from (possibly nonautonomous) algebraic dynamics which trivialise after base extension over themselves. Every wild automorphism of an abelian variety is compound fundamental isotrivial. Conversely, it is shown that the only irreducible projective varieties admitting a wild automorphism that is compound fundamental isotrivial are the abelian varieties. That is, the wild automorphism conjecture of Reichstein, Rogalski, and Zhang is here proven for compound fundamental isotrivial dynamics. Along the way, a counterexample to the naive generalisation of the conjecture to the nonautonomous setting of σ-varieties is provided.
ER  -