Finite dimensional algebras and highest weight categories.

TLDR: In this article, the authors extend this connection with finite dimensional algebra representation theory into a central theme, which they call the tilting theory of finite-dimensional algebras.

Abstract: This paper continues the program begun by us in [8]), [9] (see also [15], [18]) in which the authors have begun to exploit in the modular representation theory of semisimple algebraic groups some of the powerful techniques of the theory of derived categories. As noted in the above references, the Inspiration for this work comes both from geometry, in the form of the classic algebraic work of Bernstein-Beilinson-Deligne [1] on singular spaces and perverse sheaves, and from the tilting theory of finite dimensional algebras [2], [3], [13], [14]. The present paper broadens and extends this connection with finite dimensional algebra representation theory into a central theme.