A proper base change theorem for non-torsion sheaves in étale cohomology (Q1119981)

This note extends the proper base change theorem for torsion sheaves to the following. Given noetherian schemes with Y excellent, a proper morphism \(\pi:\quad Y\to X,\) a morphism \(f:\quad X'\to X\) whose pullback \(f':\quad Y'\to Y\) is normal, and an abelian sheaf F on Y, the base change morphisms \(f^*(R^{\bullet}\pi_*F)\to R^{\bullet}(\pi_*'f'{}^*F)\) are isomorphisms. The proof uses the original theorem, standard results on étale cohomology, and results from SGA 4 (Sém. Géométrie algébrique 4).