2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/113774This paper examines the relationship between the automorphism group of a hyperelliptic curve defined over an algebraically closed field of characteristic two and the 2-rank of the curve. In particular, we exploit the wild ramification to use the Deuring-Shafarevich formula in order to analyze the ramification of hyperelliptic curves that admit extra automorphisms and use this data to impose restrictions on the genera and 2-ranks of such curves. We also show how some of the techniques and results carry over to the case where our base field is of characteristic $p>2$.arXiv admin note: erroneously posted v2 removed at request of co-authorsNumber TheoryAlgebraic Geometrytext