On the zeroes and poles of L-functions over varieties in positive characteristic

We express the order of the pole and the leading coefficient of the -function of a (large class of) -adic coefficients ( any prime) over a quasi-projective variety over a finite field of characteristic . We use the technique of [ ] with coefficients with, as new ingredient, the use of -gauges and their equivalence, in the derived category, with Raynaud modules proved by Ekedahl.