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We study hyperelliptic curves  C  with an action of an affine group of automorphisms  G . We establish a closed form expression for the quotient curve  C / G  and for the first étale cohomology group of  C  as a representation of  G . The motivation comes from the arithmetic of hyperelliptic curves over local fields, specifically their local Galois representations and the associated invariants.

Quotients of hyperelliptic curves and Étale cohomology