Sheaf Cohomology

Abstract

As we saw in the previous chapter, a “surjection” or epimorphism $\mathfrak{f}\rightarrow \mathfrak{g}$ of sheaves need not induce a surjection of global sections. We would like to understand what further conditions are required to ensure this. Although this may seem like a fairly technical problem, it lies at the heart of many fundamental questions in geometry and function theory. Typically, we may want to know when some interesting class of functions extends from a subspace to the whole space, and this is a special case of the above problem.