Mathematical Research Letters 3, 293–297 (1996) COHOMOLOGY OF ARTIN GROUPS C. De Concini and M. Salvetti Introduction This short note is an addendum to the paper ([S]). If W is a Coxeter group, acting on C n as a reflection group, and G W is the associated Artin group (see [B], [B-S]) then (using [S 0 ]) a combinatorial complex X W was constructed (obtained very naturally from the Coxeter complex of W by identifications on the faces) which is homotopy equivalent to the orbit space Y W =  C n \  H∈A H C  / W where A is the arrangement of reflection hyperplanes of W, and H C is the complexification of H . So, when Y W is a space of type k(π, 1) (for example, when W is finite ([D]) ), X W describes the homotopy type of k(G W , 1). This topological construction was used to produce an algebraic complex which computes rank-1 local systems on X W ([S, theorem 1.10]). After looking for possible generalizations, we could almost immediately recognize that theorem 1.10 of [S] is a specialization of the general theorem below which produces very natural combinatorial formulas computing the cohomology of any local system for any Artin group (when Y W is a k(π, 1)−space). In fact, we obtain coboundary formulas which hold in the group algebra Z[G W ]. 1. The notations are similar to that of [S]. So, let (W,S ) be a Coxeter sys- tem, realized as an irreducible reflection group in R n : if A is the arrange- ment of reflection hyperplanes of W, then S will be the set of reflections with respect to the walls of a fixed chamber C 0 . Received December 6, 1995. Partially supported by M.U.R.S.T. 40%. 293