Whittaker groups generate Schottky groups yielding hyperelliptic Mumford curves of genus g; the map from the rigid space Fix_{P,m} of fixed points in good position to the space Branch_{P,m} of branch points is a rigid etale covering with Galois group (±1)^{d-1}.
van der Put, p -adic Whittaker groups , Groupe de travail d'analyse ultram\'etrique, tome 6 (1978-1979), exp
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Whittaker groups and hyperelliptic curves
Whittaker groups generate Schottky groups yielding hyperelliptic Mumford curves of genus g; the map from the rigid space Fix_{P,m} of fixed points in good position to the space Branch_{P,m} of branch points is a rigid etale covering with Galois group (±1)^{d-1}.