论文标题
有限矢量束的eTale琐事超过紧凑的复杂歧管
Etale triviality of finite vector bundles over compact complex manifolds
论文作者
论文摘要
矢量捆绑包$ e $ a $ a $ $ m $ $ m $，如果它满足具有非负积分系数的非平凡多项式方程式，则称为有限。诺里（Nori）引入有限捆绑包，证明了$ e $是有限的，并且仅当$ e $的回调$ m $ $ m $的有限étale覆盖物是琐碎的\ cite \ cite {no1}。有限束的定义自然扩展到紧凑型复杂歧管上的全态矢量束。我们证明，当$ e $将$ e $的回调对$ m $的某些有限的flotial of $ m $的覆盖物是有限的，而当$ m $ $ m $的$ m $是有限的，这是有限的。因此，$ e $是有限的，并且仅当它与有限的单片固定的骨膜连接时。
A vector bundle $E$ over a projective variety $M$ is called finite if it satisfies a nontrivial polynomial equation with nonnegative integral coefficients. Introducing finite bundles, Nori proved that $E$ is finite if and only if the pullback of $E$ to some finite étale covering of $M$ is trivializable \cite{No1}. The definition of finite bundles extends naturally to holomorphic vector bundles over compact complex manifolds. We prove that a holomorphic vector bundle over a compact complex manifold $M$ is finite if and only if the pullback of $E$ to some finite étale covering of $M$ is holomorphically trivializable. Therefore, $E$ is finite if and only if it admits a flat holomorphic connection with finite monodromy.
