Algebraic <i>K</i>-theory of projective spaces associated to Zⁿ-graded rings

In this thesis, first we generalised this result to the case of an arbitrary strongly <i>Z</i>-graded ring <i>R</i>. The projective line associated with <i>R</i> is indirectly defined by specifying the corresponding category of quasi-coherent sheaves.

The process, perhaps surprisingly, works very much like in the "classical" case with notions from algebraic geometry like sheaf cohomology and twisting sheaves being transferred to the new setting. However the aforementioned family of twisting sheaves from algebraic geometry now depends on a two-parameter construction instead of just one. Loosely following the pattern of the proof by Quillen, the <i>K</i>-theoretical splitting for the projective line is established.<br><br>We then show how this template can be expanded upon by looking at the projective plane and strongly <i>Z</i>²-graded rings.