Inspired by the work of Laumon on ε-factors and by Deligne's
1974 letter to Serre, we give an explicit cohomological definition of
ε-factors for ℓ-adic Galois representations over henselian
discrete valuation fields of positive equicharacteristic pî€ =â„“, with
(not necessarily finite) perfect residue fields. These geometric local
ε-factors are completely characterized by an explicit list of
purely local properties, such as an induction formula and the compatibility
with geometric class field theory in rank 1, and satisfy a product formula
for â„“-adic sheaves on a curve over a perfect field of characteristic p.Comment: 92 page