Abstract
We introduce a certain Artin–Schreier scheme over a finite field associated to a pair of coprime integers with divisible by the characteristic of the base field, and study the middle étale cohomology group of it. If m is even, the variety admits actions of some finite Heisenberg groups. We study the middle cohomology as representations of the Heisenberg groups. If m is odd, we compute the Frobenius eigenvalues of it concretely. This affine scheme comes from the reduction of a certain affinoid in a Lubin–Tate space.
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