中文摘要：

令X是特征为p（〉0）的代数闭域k上的一个亏格为g的一条光滑射影曲线,F∶X→X是一个绝对Frobenius态射,则当亏格g≥1时,基于由经典联络可以定义经典滤链这一理论,证明任何一个半稳定丛W的推前丛F＊W还是一个半稳定丛.同时当亏格g≥2时,基于同样的理论得到任何一个稳定丛W的推前丛F＊W还是一个稳定丛,并且诱导了两个模空间之间的态射F,F.

英文摘要：

Let X be a smooth projective curve of genus gover an algebraically field k with char（k）= p0 and F∶X→X be the absolute Frobenius morphism.When g≥1,based on the theory that we can define a canonical filtration from canonical connection,we prove that F＊W is semi-stable whenever W is semi-stable.When g≥2,base on the same theory,we also obtained that F＊W is stable bundle for any stable bundle W and induce the morphisms F,F between moduli spaces from the absolute Frobenius morphism F.