Potential isotriviality of isocrystals and proper covers
Adrian Langer, Lei Zhang
Source 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.
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