Cohomology for Picard-Vessiot theory

• DOI: 10.48550/arxiv.2308.03025
• Publication Date: 2023-01-01
• Authors: Man Cheung Tsui; Yidi Wang
• Keywords: 12H05, 16T05, 20G10, 16H05; Rings and Algebras (math.RA); FOS: Mathematics; Mathematics - Rings and Algebras

We introduce a cohomology theory that classifies differential objects arise from Picard-Vessiot theory, using the Hopf-Galois descent. To do this, we provide an explicit description of in terms torsors. then use this to give bijective correspondence between and As application, prove universal bound for splitting degree central simple algebras.