| Abstract |
(This is a seminar talk given by Mr. Joon Song, an undergraduate student, after his individual reading studies.)
In many situations one meets the same phenomenon: a short exact sequence gives rise to a long exact sequence in cohomology. However, the construction of such long exact sequences differs from case to case. In particular, the construction of the long exact sequence in sheaf theory is different from that of complexes. Is there a single framework where all long exact sequence arise in the same way? This leads to distinguished triangles which generalize the short exact sequence. In this presentation, I will introduce abelian categories, resolutions, and the derived category with their basic properties, and show how we can use the derived category briefly, through derived functor. |
