ABSTRACT
In this paper, a new derivation of the well known long exact sequence of Galois cohomology for commutative rings is presented. An attempt to incorporate much of what is known about the terms and mappings of that exact sequence into a single theory is made. A filtration of a differential, graded module gives rise not only to an exact couple and a spectral sequence, but to a more elaborate structure herein called an exact octahedron. Long exact sequences are obtained by unwinding “strands” of an exact octahedron, and relationships between the exact sequences are recorded in the exact octahedron.
