Connections on trivial vector bundles over projective schemes

Indranil Biswas; Phùng Hô Hai; João Pedro dos Santos

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arXiv · 2106.08547

Connections on trivial vector bundles over projective schemes

Indranil Biswas·Phùng Hô Hai·João Pedro dos Santos

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Abstract

Over a smooth and proper complex scheme, the differential Galois group of an integrable connection may be obtained as the closure of the transcendental monodromy representation. In this paper, we employ a completely algebraic variation of this idea by restricting attention to connections on trivial vector bundles and replacing the fundamental group by a certain Lie algebra constructed from the regular forms. In more detail, we show that the differential Galois group is a certain ``closure'' of the aforementioned Lie algebra. This is then applied to construct connections on curves with prescribed differential Galois group.

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BibTeX RIS

Indranil Biswas, Phùng Hô Hai, João Pedro dos Santos. 2021-06-16. Connections on trivial vector bundles over projective schemes. https://arxiv.org/abs/2106.08547

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