Lectures on Topics in Algebraic K-Theory

Аннотация

Algebraic K-theory has two components: the classical theory which centers around the Grothendieck group K0 of a category and uses explicit algebraic presentations, and higher algebraic K-theory which requires topological or homological machinery to define. There are three basic versions of the Grothendieck group K0. One involves the group completion construction, and is used for projective modules over rings, vector bundles over compact spaces and other symmetric monoidal categories. Another adds relations for exact sequences, and is used for abelian categories as well as exact categories; this is the version first used in algebraic geometry.