Asymptotic behavior of Ext for pairs of modules of large complexity over graded complete intersections (Q2081436)

Let \(R\) be a graded complete intersection ring, and \(M\) and \(N\) two finitely generated graded \(R\)-modules such that \(\mathrm{Ext}^{i}_{R}(M,N)\) has finite length for every \(i\geq 0\). The authors show that the even and odd Hilbert polynomials, which give the lengths of \(\mathrm{Ext}^{i}_{R}(M,N)\) for all large even \(i\) and all large odd \(i\) respectively, have the same degree and the same leading coefficient whenever the highest degree of these polynomials is at least the Krull dimension of \(M\) or \(N\). In addition, some refinements of this result are given when \(R\) is regular in small codimensions.