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

Lie-Rinehart cohomology and integrable connections on modules of rank one - Mathematics > Algebraic Geometry - Download this document for free, or read online. Document in PDF available to download.

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/