Automorphisms of congruence function fields

Martha Rzedowski-Calderón and Gabriel Daniel Villa-Salvador

Vol. 150 (1991), No. 1, 167–178

DOI: 10.2140/pjm.1991.150.167

Abstract

Let k be a finite field. For a function field K over k and m ≥ 3, it is proven that there are infinitely many non-isomorphic function fields L such that L∕K is a separable extension of degree m and Aut_kL = {Id}. It is also shown that for a finite group G, there are infinitely many non-isomorphic function fields L∕k such that Aut_kL≅G. Finally, given any finite nilpotent group G such that |G| > 1 and (|G|,|k|− 1) = 1 and any function field K over k, there are infinitely many non-isomorphic function fields L over k with Gal(L∕K) = Aut_kL≅G.

Mathematical Subject Classification 2000

Primary: 14H05

Secondary: 11R58, 14E09

Milestones

Received: 1 November 1989

Revised: 27 April 1990

Published: 1 September 1991