Program

(1) Preliminaries and motivation.

• Derived category and derived functors.
• Deligne’s intersection complex.

(2) The perverse t-structure.

• Definition and properties of t-structures.
• Examples: the standard t-structure and the perverse t-structure.
• Gluing t-structures.

(3) The intermediate extension and simple objects.

• Definition of intermediate extension.
• Simple objects in the category of perverse sheaves.

(4) The decomposition package.

• The decomposition theorem.
• Hard-Lefschetz theorem.
• The semi-simplicity theorem.

(5) Nerby and vanishing cycles.

• Construction.
• Relation with perverse sheaves.