Categorie quasi-abeliane e loro applicazioni alla geometria algebrica.

Given an abelian category A its derived category D(A) admits a natural t-structure whose heart is A. Moreover by the Auslander’s Formula A is equivalent to the quotient category of coherent functors by the Serre subcategory of effaceable functors. Given a quasi-abelian category E its derived category D(E) admits two canonical t-structures (left and right) whose hearts L and R are derived equivalent and their intersection in D(E) is E, moreover E is a tilting torsion class (rep. cotilting torsion-free class) in the right heart R (resp. L). We generalise the Auslander’s Formula to quasi-abelian categories and we extend this picture to its higher version introducing n-quasi-abelian categories. Given X a smooth algebraic variety of dimension n the category of locally free O_x-modules of finite rank is n-quasi-abelian.