Simultaneous R-equivalence of torsors: Follow-up to an article by P. Gille

[摘要] If K is a large field and G is a finite group, we show that any finite family of R-equivalent G-torsors over K is obtained by specialization from a geometrically irreducible G-torsor over an open subset of P-K(1). This answers a question of P. Gille (2001, J. Number Theory 91, 284-292). The results are also stated in terms of R-equivalence of rational points on varieties of the form GL(r, K)/G. (C) 2001 Elsevier Science.

[发布日期] 2001-12-01