关于向量丛的Frobenius下降的一个注记
A remark on Frobenius descent for vector bundles
摘要：
我们给出了一类在Spec Z上相对光滑的射影曲线上的向量丛的例子，使得对于无穷多个素约化，该丛有Frobenius下降，但对特征为零的类属纤维的限制不是半稳定的.在本文的第三部分中，我们证明了一个大类的品种（包括阿贝尔簇），任何向量丛与此Frobenius下降性质是一般半稳定的。
英文摘要：
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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