Year: 2026
Type: preprint
Abstract: 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.
Source: arXiv (Cornell University)
Authors: Langer, Adrian, Zhang, Lei
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7215066248