A Frobenius Question Related to Actions on Curves in Characteristic P

We consider which integers g can occur as the genus and of a curve defined over a field of characteristic p which admits an automorphism of degree pq, where p and q are distinct primes. This investigation leads us to consider a certain family of three-dimensional Frobenius problems and prove explicit formulas giving their solution in many cases. Required Publisher's Statement This article was published online in August 2013. Original version is available from the publisher at: http://journals.cambridge.org/action/ displayAbstract?fromPage=online&aid=9095478 This article is available at The Cupola: Scholarship at Gettysburg College: http://cupola.gettysburg.edu/mathfac/26 Glasgow Math. J. 56 (2014) 143–148. C © Glasgow Mathematical Journal Trust 2013. doi:10.1017/S0017089513000128. A FROBENIUS QUESTION RELATED TO ACTIONS ON CURVES IN CHARACTERISTIC P DARREN B. GLASS Department of Mathematics, Gettysburg College, Gettysburg, PA 17325, USA e-mail: [email protected] (Received 26 June 2012; accepted 22 January 2013; first published online 13 August 2013) Abstract. We consider which integers g can occur as the genus and of a curve defined over a field of characteristic p which admits an automorphism of degree pq, where p and q are distinct primes. This investigation leads us to consider a certain family of three-dimensional Frobenius problems and prove explicit formulas giving their solution in many cases. We consider which integers g can occur as the genus and of a curve defined over a field of characteristic p which admits an automorphism of degree pq, where p and q are distinct primes. This investigation leads us to consider a certain family of three-dimensional Frobenius problems and prove explicit formulas giving their solution in many cases. 2010 Mathematics Subject Classification. 11D07, 14G17, 11G20.