Stability of the Kato-Kuzumaki's properties under field extensions
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866911684914839552 |
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| author | Gambardella, Felipe Shaw, Harry C. |
| author_facet | Gambardella, Felipe Shaw, Harry C. |
| contents | In 1986, Kato and Kuzumaki introduced some Diophantine properties of fields, called the $C_i^q$ properties, and they hoped they would provide a good characterization of the cohomological dimension of fields. In this paper, we study the stability of some variants of the $C_i^q$ properties under transcendental and algebraic extensions. As an application, we obtain the $C_n^1$ property for the field $\mathbf{F}_p(x_1,\cdots,x_n)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_05201 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Stability of the Kato-Kuzumaki's properties under field extensions Gambardella, Felipe Shaw, Harry C. Number Theory Algebraic Geometry K-Theory and Homology 11E76, 11G20, 12G05, 12G10, 14G05, 14G27, 14J70, 19C99 In 1986, Kato and Kuzumaki introduced some Diophantine properties of fields, called the $C_i^q$ properties, and they hoped they would provide a good characterization of the cohomological dimension of fields. In this paper, we study the stability of some variants of the $C_i^q$ properties under transcendental and algebraic extensions. As an application, we obtain the $C_n^1$ property for the field $\mathbf{F}_p(x_1,\cdots,x_n)$. |
| title | Stability of the Kato-Kuzumaki's properties under field extensions |
| topic | Number Theory Algebraic Geometry K-Theory and Homology 11E76, 11G20, 12G05, 12G10, 14G05, 14G27, 14J70, 19C99 |
| url | https://arxiv.org/abs/2511.05201 |