Felipe Gambardella

activity

20232026

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math.NT2025

Stability of the Kato-Kuzumaki's properties under field extensions

Felipe Gambardella, Harry C. Shaw

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 cohomol…

math.AG2025

Kato-Kuzumaki's properties for function fields over higher local fields

Felipe Gambardella

Let $k$ be a $d$ -local field such that the corresponding $1$ -local field $k^{(d - 1)}$ is a $p$ -adic field and $C$ a curve over $k$ . Let $K$ be the function field of $C$ . We prove th…