Vol. 20, No. 1, 1967

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Another proof of a theorem on rational cross sections

Maxwell Alexander Rosenlicht

Vol. 20 (1967), No. 1, 129–133

The extant proofs of the existence of a rational cross section for a transformation space for a connected solvable linear algebraic group either use a certain amount of algebraic curve theory or restrict themselves to the case of a principal space, where the question is one of galois cohomology, the result being equivalent to the statement that H1(G,k) = 0 for G a k-solvable linear algebraic group. The present proof of the general result may be considered more elementary in that it depends only on the standard facls on fields of rationality of algebraic sets.

Mathematical Subject Classification
Primary: 14.50
Received: 6 February 1966
Published: 1 January 1967
Maxwell Alexander Rosenlicht