Benjamin Briggs

ABSTRACT

The Eagon resolution presents the minimal free resolution of the residue field of a Golod ring in a strikingly simple way. For example, using this presentation, it was recently observed (by Cuong, Dao, Eisenbud, Kobayashi, Polini, and Ulrich) that the residue field of a Golod ring has only finitely many isomorphism classes of indecomposable syzygy summands.

I will talk about (1) how to conceptually view the Eagon resolution as arising from a bar construction, and (2) how to generalise this to minimal Eagon-like resolutions over many other classes of local rings (the so-called “Cohen Koszul” rings).

This is joint work with Claudia Miller, Hamid Rahmati, and Zheng Yang.