The K-Functor in Algebraic Geometry
In the previous chapter we described the geometry of regular morphisms. Here we describe one part of their homology, namely the K-functor on the category of locally free sheaves (which are always assumed to be of finite rank). An arbitrary locally free sheaf does not behave well under the direct image. Fortunately, the K-group generated by the locally free sheaves is also generated by a subfamily of sheaves which do behave well, and which we call regular sheaves. We use a cohomological characterization for these, due to Mumford.
KeywordsExact Sequence Short Exact Sequence Free Resolution Coherent Sheave Coherent Sheaf
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