Koszul-Tate Resolutions and Cotangent Cohomology for Monomial Ideals

Abstract: Introduced by Tate in 1957, a Koszul-Tate resolution allows one to replace any algebra with a free differential graded algebra. This can be used to compute important invariants of the original algebra such as BRST cohomology or cotangent cohomology. I will report on a re-interpretation of recent work by Hancharuk, Laurent-Gengoux, and Strobl that constructs explicit Koszul-Tate resolutions. Using this, I will then discuss some work in progress on higher cotangent cohomology for quotients of polynomial rings by monomial ideals. This is joint with Francesco Meazzini and Andrea Petracci. No prior knowledge of Koszul-Tate resolutions or cotangent cohomology is assumed.

algebraic geometrynumber theory

Audience: researchers in the discipline

SFU NT-AG seminar

Series comments: The Number Theory and Algebraic Geometry (NT-AG) seminar is a research seminar dedicated to topics related to number theory and algebraic geometry hosted by the NT-AG group (Nils Bruin, Imin Chen, Stephen Choi, Katrina Honigs, Nathan Ilten, Marni Mishna).

We acknowledge the support of PIMS, NSERC, and SFU.

For Fall 2025, the organizers are Katrina Honigs and Peter McDonald.

We normally meet in-person in the indicated room. For online editions, we use Zoom and distribute the link through the mailing list. If you wish to be put on the mailing list, please subscribe to ntag-external using lists.sfu.ca