Editing K-theory (section)

=== Grothendieck group of vector bundles in algebraic geometry ===
There is an analogous construction by considering vector bundles in [[algebraic geometry]]. For a [[Noetherian scheme]] <math>X</math> there is a set <math>\text{Vect}(X)</math> of all isomorphism classes of [[algebraic vector bundle]]s on <math>X</math>. Then, as before, the direct sum <math>\oplus</math> of isomorphisms classes of vector bundles is well-defined, giving an abelian monoid <math>(\text{Vect}(X),\oplus)</math>. Then, the Grothendieck group <math>K^0(X)</math> is defined by the application of the Grothendieck construction on this abelian monoid.