Jan 13 2021

Commutative Algebra Seminar: Some homological characterisations of complete intersections, by Benjamin Briggs

January 13, 2021

4:00 PM - 4:50 PM

Location

Zoom

Address

Chicago, IL

Benjamin Briggs (University of Utah): Some homological characterisations of complete intersections

For any ideal I of finite projective dimension in a local ring R, Vasconcelos conjectured that I is complete intersection if and only if the conormal module I/I^2 has finite projective dimension over R/I. Quillen made a similar conjecture earlier: I is complete intersection if and only if the cotangent complex of R/I over R has finite projective dimension (this was established by Avramov in 1999).

I'll try to explain why the similarity between these conjectures is not just superficial, and how you can in fact prove a result generalising the two about "higher conormal modules" (I'll explain what these are, and also give some background on the cotangent complex). This is joint work with Srikanth Iyengar.

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Contact

Wenliang Zhang

Date posted

Jan 19, 2021

Date updated

Jan 19, 2021

Speakers

Benjamin Briggs | (University of Utah)