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arXiv · 2207.05860

A note on projective dimension over twisted commutative algebras

Steven V Sam·Andrew Snowden
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Abstract

Let $M$ be a finitely generated module over a free twisted commutative algebra $A$ that is finitely generated in degree one. We show that the projective dimension of $M({\bf C}^n)$ as an $A({\bf C}^n)$-module is eventually linear as a function of $n$. This confirms a conjecture of Le, Nagel, Nguyen, and R\"omer for a special class of modules.

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Steven V Sam, Andrew Snowden. 2022-07-12. A note on projective dimension over twisted commutative algebras. https://doi.org/10.1216/jca.2026.18.121

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