Non-conservative function fields of genus \((p+1)/2\) (Q912936)

Let \(F/K\) be a separably generated function field in one variable of genus \(g\) and positive characteristic \(p\geq 5\). It is called conservative if \(g=\bar g=\) genus of \(F\bar K/\bar K\) \((\bar K=\) algebraic closure of \(K\)). The defect \(g-\bar g\) is always divisible by \((p-1)/2\). The authors study the first nontrivial case where \(\bar g=1\) and \(g=(p+1)/2\). In their main result, they describe a normal form for such \(F/K\), and moreover, they give criteria for \(F/K\) to be hyperelliptic, and compute its automorphism group.