Conference abstracts

Session S10 - Homological Methods

July 28, 18:00 ~ 18:30

## Relative Igusa-Todorov functions

### Universidad de la República, Uruguay   -   marclan@fing.edu.uy

We develop the theory of the $\mathcal{E}$-relative Igusa-Todorov functions in an exact IT-context $(\mathcal{C},\mathcal{E})$. In the case when $\mathcal{C}=$mod$\, (\Lambda)$ is the category of finitely generated left $\Lambda$-modules, for an artin algebra $\Lambda,$ and $\mathcal{E}$ is the class of all exact sequences in $\mathcal{C},$ we recover the usual Igusa-Todorov functions. We use the setting of the exact structures and the Auslander-Solberg relative homological theory to generalise the original Igusa-Todorov's results. Furthermore, we introduce the $\mathcal{E}$-relative Igusa-Todorov dimension and also we obtain relationships with the relative global and relative finitistic dimensions and the Gorenstein homological dimensions.

Joint work with Octavio Mendoza (Universidad Nacional Autónoma de México).