Abstract
In 1986, Kato and Kuzumaki stated several conjectures in order to give a diophantine characterization of cohomological dimension of fields in terms of projective hypersurfaces of small degree and Milnor -theory. We establish these conjectures for finite extensions of and , and we prove new local-global principles over number fields and global fields of positive characteristic in the context of Kato and Kuzumaki’s conjectures.
Citation
Diego Izquierdo. "On a conjecture of Kato and Kuzumaki." Algebra Number Theory 12 (2) 429 - 454, 2018. https://doi.org/10.2140/ant.2018.12.429
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