Carlos Parra, Universidad Austral
de Chile, Valdivia

Title: FP$_{n}$ injective objects in Grothendieck categories with a projective generator

Title: FP$_{n}$ injective objects in Grothendieck categories with a projective generator

Abstract: We aim to generalize
the theory of torsion pairs from FP$_{n}$-injective and FP$_{n}$-flat modules over
$n$-hereditary rings to the context of Grothendieck categories
with enough idempotents. In this setting, we show that the class
of FP$_{n}$-injective objects is
a torsion class if, and only if, the projective dimension of
each FP$_{n}$ object is less than
2. Moreover, we show that the class of FP$_{n}$-injective complexes over a
ring is never a torsion class, along with some applications of
our general approach to the category of functors from a small
preadditive category to the category of abelian groups.

This is a joint work-in-progress with D. Bravo, S. Odabasi and M. Perez. This work has been supported by the grant CONICYT/FONDECYT/Iniciacion/11160078.