# Lie-Rinehart cohomology and integrable connections on modules of rank one - Mathematics > Algebraic Geometry

Abstract: Let \$k\$ be an algebraically closed field of characteristic 0, let \$R\$ be acommutative \$k\$-algebra, and let \$M\$ be a torsion free \$R\$-module of rank onewith a connection \$ abla\$. We consider the Lie-Rinehart cohomology with valuesin \$End {R}M\$ with its induced connection, and give an interpretation of thiscohomology in terms of the integrable connections on \$M\$. When \$R\$ is anisolated singularity of dimension \$d\geq2\$, we relate the Lie-Rinehartcohomology to the topological cohomology of the link of the singularity, andwhen \$R\$ is a quasi-homogenous hypersurface of dimension two, we give acomplete computation of the cohomology.

Author: Eivind Eriksen, Trond Stølen Gustavsen

Source: https://arxiv.org/