The eventual shape of Betti tables of powers of ideals
Abstract
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.
 Publication:

arXiv eprints
 Pub Date:
 October 2011
 arXiv:
 arXiv:1110.0383
 Bibcode:
 2011arXiv1110.0383B
 Keywords:

 Mathematics  Commutative Algebra;
 Mathematics  Algebraic Geometry;
 13D45;
 13D02
 EPrint:
 15 pages