Koszul homomorphisms and universal resolutions in local algebra

Janina Letz (U. Bielefeld and UCLA)
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.

Event Type