Asymptotic behavior of Ext for pairs of modules of large complexity over graded complete intersections
Abstract
Let $M$ and $N$ be finitely generated graded modules over a graded complete intersection $R$ such that $\operatorname{Ext}_R^i(M,N)$ has finite length for all $i\gg 0$. We show that the even and odd Hilbert polynomials, which give the lengths of $\operatorname{Ext}^i_R(M,N)$ 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.
- Publication:
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arXiv e-prints
- Pub Date:
- December 2020
- DOI:
- 10.48550/arXiv.2012.10670
- arXiv:
- arXiv:2012.10670
- Bibcode:
- 2020arXiv201210670J
- Keywords:
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- Mathematics - Commutative Algebra
- E-Print:
- Minor edits. Final version, to appear in Mathematische Zeitschrift