Janina Letz (U. Bielefeld and UCLA)
Tuesday, March 5, 2024 - 2:30pm
PDL C-38
Title: Koszul homomorphisms and universal resolutions in local algebra
Abstract: I will define a Koszul property for a homomorphism of local
rings $\varphi \colon Q \to R$. Koszul homomorphisms have good
homological properties. Using $\mathrm{A}_\infty$-structures one can
construct universal free resolutions of $R$-modules from free
resolutions over $Q$, generalizing the classical construction by
Priddy. This recovers the resolutions of Shamash and Eisenbund for
complete intersection homomorphisms and the resolutions of Iyengar and
Burke for Golod homomorphisms. This is based on work with Ben Briggs,
James Cameron and Josh Pollitz.