2021/06/16 by Indranil Biswas, Biswas, Indranil, Phùng Hô Hái +3
Mathematics · Medicine · Physics and Astronomy · #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Cancer Treatment and Pharmacology #Differential Geometry (math.DG) #FOS: Mathematics #Nonlinear Waves and Solitons
paper · pdf · doi:10.48550/arxiv.2106.08547
openalex publication_date 2021/06/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.