Relative Koszul Duality

I have been working on a project, since 2013, to generalize Koszul duality, as formulated by Lefèvre-Hasegawa and Positselski, to work over an arbitrary commutative base ring.

This page is a collection of work related to the project, which is very much still in progress.

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The slides below, from Dave Benson's birthday conference, give an overview:

• Generalized Koszul duality applied to complete intersection rings.

The first two foundational papers are:

• Strictly unital A-infinity algebras, to appear in JPAA.


• Transfer of A-infinity structures to projective resolutions.

The first application to homological commutative algebra is in:

• Golod rings and higher homotopies.

A draft from late 2014 is below; the first three sections of this have become the two foundational papers above:

• Koszul duality for representations of an A-infinity algebra defined over a commutative ring.

Some other writings related to the project:

• Research statement, from 2014.


• Summary of NSF proposal, from 2013 (was not funded).


• Description from same NSF proposal.