Students' Algebraic Geometry Seminar : Triangle Power

The derived category is no longer an abelian category, so we need to find some other structure to work with. In this talk we will define the notion of a triangulated category, wherein distinguished triangles roughly replace the role of short exact sequences. We will see how triangulated categories can be broken up into simpler pieces via semi-orthogonal decompositions, and we will discuss semi-orthogonal decompositions for the derived categories of projective spaces and blowups.