2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/68045Consider the ring $R:=\Q[τ,τ^{-1}]$ of Laurent polynomials in the variable $τ$. The Artin's Pure Braid Groups (or Generalized Pure Braid Groups) act over $R,$ where the action of every standard generator is the multiplication by $τ$. In this paper we consider the cohomology of such groups with coefficients in the module $R$ (it is well known that such cohomology is strictly related to the untwisted integral cohomology of the Milnor fibration naturally associated to the reflection arrangement). We give a sort of \textit{stability} theorem for the cohomologies of the infinite series $A$, $B$ and $D,$ finding that these cohomologies stabilize, with respect to the natural inclusion, at some number of copies of the trivial $R$-module $\Q$. We also give a formula which compute this number of copies.17 pages; added reference for section 1Group TheoryCategory Theory20J06 (20F36)text