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

Let M and N be finitely generated graded modules over a graded complete intersection R such that ExtRi(M,N)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\text {Ext}}_R^i(M,N)$$\end{document} has finite length for all i≫0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$i\gg 0$$\end{document}. We show that the even and odd Hilbert polynomials, which give the lengths of ExtRi(M,N)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\text {Ext}}^i_R(M,N)$$\end{document} for all large even i and all large odd i, have the same degree and leading coefficient whenever the highest degree of these polynomials is at least the dimension of M or N. Refinements of this result are given when R is regular in small codimensions.