2005/02/09 by Jean-Louis Colliot-Thélène, Colliot-Thélène, Jean-Louis
Mathematics · #11E76 #12G10 #14C35 #14G05 #14J26 #Algebraic Geometry (math.AG) #FOS: Mathematics #K-Theory and Homology (math.KT) #math.AG #math.KT #msc:11E76 #msc:12G10 #msc:14C35 #msc:14G05 #msc:14J26
paper · pdf · doi:10.48550/arxiv.math/0502194
5 pages, in English
arxiv created 2005/02/09 · arxiv updated 2009/12/01
Ax gave examples of fields of cohomological dimension 1 which are not C1-fields. Kato and Kuzumaki asked whether a weak form of the C1-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 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>3, I use forms of degree p in p+1 variables.