Tuesday, March 17, 14:00, 7.527

Simone Virili (Barcelona), Lengths, ranks, and Gabriel dimension

Abstract:
In the first part of the talk we will recall a few classical results about length functions in Grothendieck categories, proved by Peter Vámos in the sixties. More concretely, we will show that there is a bijective correspondence between irreducible discrete length functions and the points of the so-called atom spectrum, recently introduced by Kanda, and we will use this to classify all length functions in categories with Gabriel dimension.
In the second part of the talk, we will apply these results to the functor category of a ring, reobtaining as a corollary several results due to Crawley-Boevey, Schofield, and Herzog.