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- W2002000222 abstract "Let G be a linear algebraic group and X be an irreducible algebraic variety with a generically free G -action, all defined over an algebraically closed base field of characteristic zero. It is well known that X can be viewed as a G -torsor, representing a class [ X ] in H 1 ( K , G ), where K is the field of G -invariant rational functions on X . We have previously shown that if X has a smooth H -fixed point for some non-toral diagonalizable subgroup H of G then [ X ]≠1. It is natural to ask if the converse is true, assuming G is connected and X is projective and smooth. In this note we show that the answer is “no.”" @default.
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- W2002000222 date "2003-05-01" @default.
- W2002000222 modified "2023-09-29" @default.
- W2002000222 title "A non-split torsor with trivial fixed point obstruction" @default.
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- W2002000222 doi "https://doi.org/10.1016/s0021-8693(03)00171-6" @default.
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