Sign (di)lemma for dimension shifting

Abstract

There is a surprising occurrence of some minus signs in the isomorphisms produced in the well-known technique of dimension shifting in calculating derived functors in homological algebra. We explicitly determine these signs. Getting these signs right is important in order to avoid basic contradictions. We illustrate the result - which we call as the sign lemma for dimension shifting - by some de Rham cohomology and Chern class considerations for compact Riemann surfaces.