Higgs bundles and fundamental group schemes

Indranil Biswas; Ugo Bruzzo; Sudarshan Gurjar

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arXiv · 1607.07207

Higgs bundles and fundamental group schemes

Indranil Biswas·Ugo Bruzzo·Sudarshan Gurjar

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Abstract

Relying on a notion of "numerical effectiveness" for Higgs bundles, we show that the category of "numerically flat" Higgs vector bundles on a smooth projective variety $X$ is a Tannakian category. We introduce the associated group scheme, that we call the "Higgs fundamental group scheme of $X$," and show that its properties are related to a conjecture about the vanishing of the Chern classes of numerically flat Higgs vector bundles.

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Indranil Biswas, Ugo Bruzzo, Sudarshan Gurjar. 2016-07-25. Higgs bundles and fundamental group schemes. https://arxiv.org/abs/1607.07207

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