Part-I:

We will discuss examples of torsion pairs in various abelian categories, the resulting t-structures on the derived categories, and see the corresponding truncation functors in action. The examples will come from commutative algebra and algebraic geometry.

 

Part-II:

We will consider elliptic fibrations, and see how the geometry gives rise to various torsion pairs and t-structures on the derived categories of coherent sheaves involved.