—The Seventh Epoch

Since 1945, the considerable advances in algebraic topology, differential topology, and the theory of analytic spaces, due to the introduction of the notions of sheaf, of cohomology with coefficients in a sheaf, and of spectral sequence (all three invented by J. Leray), have also completely renovated the concepts and the methods of algebraic geometry, “classical” as well as “abstract.” The language of cohomology permits the unification and simplification of many definitions and results, and opens the way for the solution of numerous problems.