Editing K-theory (section)

=== K<sub>0</sub> of a field ===
The easiest example of the Grothendieck group is the Grothendieck group of a point <math>\text{Spec}(\mathbb{F})</math> for a field <math>\mathbb{F}</math>. Since a vector bundle over this space is just a finite dimensional vector space, which is a free object in the category of coherent sheaves, hence projective, the monoid of isomorphism classes is <math>\N</math> corresponding to the dimension of the vector space. It is an easy exercise to show that the Grothendieck group is then <math>\Z</math>.