Document Type

Article

Publication Date

2009

Department

Mathematics

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.

Required Publisher's Statement

Original version available from the publisher at: http://www.worldscientific.com/doi/abs/10.1142/S1793042109002468

Included in

Mathematics Commons

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