Wild ramification and K(pi,1) spaces

I will sketch the proof that every connected affine scheme in positivecharacteristic is a K(pi,1) space for the etale topology. The keytechnical ingredient is a ?RoeBertini-type?R statement regarding the wildramification of l-adic local systems on affine spaces. Its proof usesin an essential way recent advances in higher ramification theory dueto T. Saito.