For finitely generated modules M over free twisted commutative algebras A generated in degree one, the projective dimension of M(C^n) as an A(C^n)-module is eventually linear in n.
Equivariant Hilbert series in non-noetherian polynomial rings
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A note on projective dimension over twisted commutative algebras
For finitely generated modules M over free twisted commutative algebras A generated in degree one, the projective dimension of M(C^n) as an A(C^n)-module is eventually linear in n.