Potential isotriviality of isocrystals and proper covers

@misc{langer2026potential,
  title = {{Potential isotriviality of isocrystals and proper covers}},
  author = {Adrian Langer and Lei Zhang},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.39815},
  eprint = {2609.39815},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.39815},
}

TY  - UNPB
TI  - Potential isotriviality of isocrystals and proper covers
AU  - Adrian Langer
AU  - Lei Zhang
PY  - 2026
DA  - 2026/09/30
PB  - arXiv
DO  - 10.48550/arxiv.2609.39815
UR  - https://arxiv.org/abs/2609.39815
AB  - We study convergent and overconvergent isocrystals that become trivial after pullback along a proper surjective morphism. On a geometrically unibranch variety over an algebraically closed field, every such object is already trivialized by a finite étale cover. Over a perfect field, this shows that a proper cover giving geometric triviality can be replaced by a finite étale cover over the ground field, and implies finiteness of the geometric monodromy group. For proper geometrically unibranch varieties, finite geometric monodromy is also sufficient. In the overconvergent case, a dominant morphism can replace the given proper cover. A nodal curve shows why the geometrically unibranch hypothesis is needed.
ER  -