An introduction to field extensions and Galois descent for sheaves of vector spaces

We study extension of scalars for sheaves of vector spaces, assembling results that follow from well-known statements about vector spaces, but also developing some complements. In particular, we formulate Galois descent in this context, and we also discuss the case of derived categories and perverse sheaves. Most of the results are not new, but our aim is to give an accessible introduction to this subject relying only on techniques from basic sheaf theory. Our proofs also illustrate some applications of results about the structure of constructible and perverse sheaves.