Cohomology of finite modules over short Gorenstein rings
Menning, Melissa · Sega, Liana
Original · EN
Let R be a Gorenstein local ring with maximal ideal m satisfying m³=0². Set k=R/m and e=rankₖ(m/m²). If e>2 and M, N are finitely generated R-modules, we show that the formal power series ∑ᵢ₌₀ₖ(Extⁱᵣ(M,N)⊗ᵣ k)tⁱ and ∑ᵢ₌₀ₖ(Torᵢʳ(M,N)⊗ᵣ k)tⁱ are rational, with denominator 1-et+t².
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