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The 2-ranks of Hyperelliptic Curves with Extra Automorphisms

Darren Glass
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Abstract

This 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 $p>2$.

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BibTeXRIS

Darren Glass. 2006-08-07. The 2-ranks of Hyperelliptic Curves with Extra Automorphisms. https://arxiv.org/abs/math/0606113

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