A remark on Frobenius descent for vector bundles

Details A remark on Frobenius descent for vector bundles A remark on Frobenius descent for vector bundles

2007-09-11

arxiv.org/abs/0709.1677v2

Mathematics

Algebraic Geometry

Final version. Several changes and improvements. In particular, we added the comments of the referee which helped to simplify

Scientific paper

We give a class of examples of vector bundles on a relative smooth projective curve over Spec Z such that for infinitely many prime reductions the bundle has a Frobenius descent, but the restriction to the generic fiber in characteristic zero is not semistable. In the third section of the paper we prove for a large class of varieties (including abelian varieties) that any vector bundle with this Frobenius descent property is generically semistable.

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