 Fix a prime number ℓ which is invertible in "k".Consider the ℓ-adic cohomology groups (coefficients in the ℓ-adic integers Zℓ, scalars then extended to the ℓ-adic numbers Qℓ) of the base extension of "V" to "k"s; these groups are representations of "G".For any "i" ≥ 0, a codimension-"i" subvariety of "V" (understood to be defined over "k") determines an element of the cohomology group

which is fixed by "G".