ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

2. Algebra

1991 MS Classification: 13, 12 Kang, Ming-Chang, National Taiwan University, Taiwan Rationality of Some Projective Linear Actions Let K be any field, V a finite-dimensional vector space over K, σ ∈ GL(V) where the order of σ can be finite or infinite. Note that it is unnecessary to assume that K is algebraically closed. Theorem. If K(V) and K(P(V)) denote the function fields of V and P(V) respectively, then both K(V)^{<σ>} and K(P(V))^{<σ>} are rational (= purely transcendental) over K, provided that dim_{K} V ≤ 3. Similar results hold for a cyclic affine action. This is a joint work with H. Ahmad and M. Hajja.