Rees' theorem for filtrations, multiplicity function and reduction criteria

Parangama Sarkar

Let $J\subset I$ be ideals in a formally equidimensional local ring with $\lambda (I/J)<\infty .$ Rees proved that for all $n\gg 0$, $\lambda (I^n/J^n)$ is a polynomial $P(I/J)(X)$ in $n$ of degre…