A remark on Frobenius descent for vector bundles
Abstract
Description
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.
Final version. Several changes and improvements. In particular, we added the comments of the referee which helped to simplify the proof of Lemma 2.1 and to clarify Example 2.5 via Lemma 2.4. To appear in Michigan Math. J. 2008
Final version. Several changes and improvements. In particular, we added the comments of the referee which helped to simplify the proof of Lemma 2.1 and to clarify Example 2.5 via Lemma 2.4. To appear in Michigan Math. J. 2008