# 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 - Descarga este documento en PDF. Documentación en PDF para descargar gratis. Disponible también para leer online.

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.

Autor: Eivind Eriksen, Trond Stølen Gustavsen

Fuente: https://arxiv.org/