Séance Séminaire

Séminaire Algèbre Géométrie Algébrique Topologie Algébrique

Tilting theory and the finitistic dimension conjectures

For a finite-dimensional algebra $\Lambda$ the little finitistic dimension findim$\Lambda$ is defined as the supremum of the projective dimensions attained on the category ${\cal P}^{{<\infty}}$ of all finitely generated $\Lambda$-modules of finite projective dimension, while the big finitistic dimension Findim$\Lambda$ is defined correspondingly on the category of all $\Lambda$-modules of finite projective dimension. The Finitistic Dimension Conjectures ask when these dimensions coincide (this is known to fail in general), and moreover, whether the little finitistic dimension is always finite. I will discuss a new approach to these conjectures using infinite dimensional tilting modules. Hereby I will present joint work with Jan Trlifaj.