2008/10/16 by Eivind Eriksen, Eriksen, Eivind, Trond Stølen Gustavsen +1
Mathematics · #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #Commutative Algebra (math.AC) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Representation Theory (math.RT) #math.AC #math.AG #math.RT
paper · pdf · doi:10.48550/arxiv.0810.2926
13 pages
arxiv created 2008/10/16 · openalex publication_date 2008/10/16 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let k be an algebraically closed field of characteristic 0, let R be a commutative k-algebra, and let M be a torsion free R-module of rank one with a connection ∇. We consider the Lie-Rinehart cohomology with values in EndR(M) with its induced connection, and give an interpretation of this cohomology in terms of the integrable connections on M. When R is an isolated singularity of dimension d≥2, we relate the Lie-Rinehart cohomology to the topological cohomology of the link of the singularity, and when R is a quasi-homogenous hypersurface of dimension two, we give a complete computation of the cohomology.