Orateur : Antoine Caradot
Établissement : Université de Saint-Etienne (France)
Dates : 2025-09-11 – 2025-09-11
Heures : 14:00 – 14:00
Lieu : Salle 0-6
Résumé :
In order to study the (co)homological properties of a local ring $R$, one can look at a resolution of the residue field of $R$. This can be achieved by a process due to Tate, where the resulting chain complex is a differential graded (dg) algebra with a divided power (pd) structure. Moreover, it is known that the cohomology of the dual of this chain complex, the Yoneda algebra of $R$, is the enveloping algebra of a Lie algebra called the homotopy Lie algebra. Using the Hopf algebra structure of the Tor algebra of $R$, we will explain how the pd-derivations of the resolution are related to the homotopy Lie algebra of $R$. This provides a way to look at the cohomology of $R$ by only looking at particular endomorphisms of the resolution, thus not requiring the use of cocycles and coboundaries. This is joint work with Zongzhu Lin.