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.
This is the author's version of the work. This publication appears in Gettysburg College's institutional repository by permission of the copyright owner for personal use, not for redistribution.
Glass, Darren B. “The 2-ranks of Hyperelliptic Curves With Extra Automorphisms” International Journal of Number Theory 2009. 5(5):1-14
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Original version available from the publisher at: http://www.worldscientific.com/doi/abs/10.1142/S1793042109002468