Quotients of hyperelliptic curves and etale cohomology
arXiv:1510.08880 · doi:10.1093/qmath/hax053
Abstract
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 etale 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.
21 pages