We show that under some assumptions on the monodromy group some combinations of higher Chern classes of a flat vector bundle are torsion in the Chow group. Similar results hold for flat vector bundles that deform to such flat vector bundles (also in case of quasi-projective varieties). The results are motivated by Bloch’s conjecture on Chern classes of flat vector bundles on smooth complex projective varieties but in some cases they give a more precise information. We also study Higgs version of Bloch’s conjecture and analogous problems in the positive characteristic case.

中文翻译：

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平面向量丛的代数陈氏类

我们证明，在单向群的某些假设下，平面向量丛的较高陈类的某些组合在 Chow 群中是挠率。类似的结果适用于变形为此类平面向量丛的平面向量丛（也在准射影簇的情况下）。这些结果的动机是布洛赫对光滑复射影簇上的平面向量丛陈氏类的猜想，但在某些情况下它们给出了更精确的信息。我们还研究了布洛赫猜想的希格斯版本以及正特征情况下的类似问题。