Connections on trivial vector bundles over projective schemes
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.
Keywords
Cite
@article{arxiv.2106.08547,
title = {Connections on trivial vector bundles over projective schemes},
author = {Indranil Biswas and Phùng Hô Hai and João Pedro dos Santos},
journal= {arXiv preprint arXiv:2106.08547},
year = {2023}
}
Comments
A reader pointed out an error; we have removed the results concerning applications to the connections on the projective line. To appear in C. R. Math. Acad. Sci. Paris