Fields of cohomological dimension one versus C1-fields J.-L. Colliot-Thélène
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Fields of cohomological dimension one versus C 1-fields J.-L. Colliot-Théì ene Summary. Ax gave examples of fields of cohomological dimension 1 which are not C 1-fields. Kato and Kuzumaki asked whether a weak form of the C 1-property holds for all fields of cohomological dimension 1 (existence of solutions in extensions of coprime degree rather than existence of a solution in the ground field). Using work of Merkur ' ev and Suslin , and of Rost , D. Madore and I recently produced examples which show that the answer is in the negative. In the present note , I produce examples which require less work than the original ones. In the original paper , some of the examples were given by forms of degree 3 in 4 variables. Here , for an arbitrary prime p ≥ 5 , I use forms of degree p in p + 1 variables .
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