Extensions of sheaves of commutative algebras by nontrivial kernels

Donovan Harold Van Osdol

Vol. 55 (1974), No. 2, 531–541

DOI: 10.2140/pjm.1974.55.531

Abstract

Let A, M, and R be sheaves of commutative algebras on a topological space. Given a surjection from R to M there is associated a cohomology class in H²(R,ZA), the second bicohomology group of R with coefficients in the center of A. This cohomology class is zero if and only if the original surjection arises from an extension of R by A.

Mathematical Subject Classification

Primary: 18H20

Milestones

Received: 16 January 1973

Published: 1 December 1974