The eventual shape of Betti tables of powers of ideals

@article{Bagheri2011TheES,
  title={The eventual shape of Betti tables of powers of ideals},
  author={A. Bagheri and M. Chardin and H. H{\`a}},
  journal={arXiv: Commutative Algebra},
  year={2011}
}
  • A. Bagheri, M. Chardin, H. Hà
  • Published 2011
  • Mathematics
  • arXiv: Commutative Algebra
  • Let $G$ be a finitely generated abelian group, and let $S = A[x_1, ..., x_n]$ be a $G$-graded polynomial ring over a commutative ring $A$. Let $I_1, ..., I_s$ be $G$-homogeneous ideals in $S$, and let $M$ be a finitely generated $G$-graded $S$-module. We show that, when $A$ is Noetherian, the nonzero $G$-graded Betti numbers of $MI_1^{t_1} ... I_s^{t_s}$ exhibit an asymptotic linear behavior as the $t_i$s get large. 
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