Algebraic Geometry and K-Theory

General concepts and structures studied by algebraic geometry and K-theory, the branch that treats solution sets of polynomial equations as geometric objects in their own right. Belongs here: the Algebraic Variety, the zero locus of a system of polynomial equations, the field's basic object of study; the Scheme, the generalization of a variety built by gluing together spectra of commutative rings, which lets the field handle nilpotents and arithmetic base rings the classical variety cannot; the Sheaf, the bookkeeping device that assigns compatible local data, such as regular functions, to the open sets of a variety or scheme, letting local information be patched into a global one. Does not belong here: the branch entity Algebraic Geometry and K-Theory itself, and named individual mathematical objects belonging to this cluster, which are typed as mathematical-object rather than concept even when they use these same underlying structures.