TY - JOUR AU - de Freitas, Thiago Henrique AU - PĂ©rez, Victor Hugo Jorge AU - Lima, Pedro Henrique PY - 2021/08/31 Y2 - 2024/03/28 TI - Asymptotic behavior of $j$-multiplicities JF - MATHEMATICA SCANDINAVICA JA - Math. Scand. VL - 127 IS - 2 SE - Articles DO - 10.7146/math.scand.a-126029 UR - https://www.mscand.dk/article/view/126029 SP - 209-222 AB - <p>Let $R= \oplus_{n\in \mathbb{N}_0}R_n$ be a Noetherian homogeneous ring with local base ring $(R_0,\mathfrak{m}_0)$. Let $R_+= \oplus_{n\in \mathbb{N}}R_n$ denote the irrelevant ideal of $R$ and let $M=\oplus_{n\in \mathbb{Z}}M_n$ be a finitely generated graded $R$-module. When $\dim(R_0)\leq 2$ and $\mathfrak{q}_0$ is an arbitrary ideal of $R_0$, we show that the $j$-multiplicity of the graded local cohomology module $j_0({\mathfrak{q}_0},H_{R_+}^i(M)_n)$ has a polynomial behavior for all $n\ll0$.</p> ER -