Teoría $K$ de categorías de complejos y aplicaciones

We apply, following Gillet, Thomason ant others, Waldhausen’s Algebraic $K$-theory to categories of complexes. This permits a treatment of Higher Algebraic $K$-theory of schemes in the spirit of Grothendieck (SGA 6) and as a consequence it results the covariance of $K$-theory of coherent sehaves for proper morphisms. We introduce a bivariant Algebraic $K$-theory, solving a question of Fulton-MacPherson.