The rationality problem for purely monomial group actions

Hidetaka Kitayama

Vol. 253 (2011), No. 1, 95–102

DOI: 10.2140/pjm.2011.253.95

Abstract

We investigate the rationality problem for purely monomial actions of finite groups. We solve it affirmatively in the following case: K is a field with char K≠2 and G is a subgroup of GL(n; ℤ) isomorphic to (C₂)ⁿ, where n > 0. Then the fixed field of K(x₁,…x_n) under the purely monomial action of G is rational over K.

Keywords

rationality problem, purely monomial, finite group action

Mathematical Subject Classification 2000

Primary: 12F20, 13A50, 14E08

Milestones

Received: 21 October 2010

Revised: 19 November 2010

Accepted: 26 November 2010

Published: 28 November 2011

Proposed: Alexander S. Merkurjev