Characteristic Class And The Epsilon-Factor Of An Etale Sheaf

We prove a twist formula for the epsilon-factor of a constructible sheaf on a projective smooth variety over a finite field in terms of characteristic class of the sheaf. This formula is a modified version of the formula conjectured by Kato and Saito in [Ann. of Math. 168 (2008), pp. 33-96].We give two applications of the twist formula. First, we prove that the characteristic classes of constructible etale sheaves on projective smooth varieties over a finite field are compatible with proper push-forward. Secondly, we show that the two Swan classes in the literature are the same on proper smooth surfaces over a finite field.