Rationally connected varieties over the maximally unramified extension of \(p\)-adic fields (Q1697454)

The paper under review proves that a smooth projective rationally connected variety with the Hilbert polynomial \(P\) over the maximally unramifed extension of the \(p\)-adics always admits rational points when \(p\) does not belong a finite set of primes depending only upon \(P\). The proof uses mathematical logic similiar to \textit{J. Ax} and \textit{S. Kochen}'s result [Am. J. Math. 87, 605--630, 631--648 (1965; Zbl 0136.32805)], which states that the \(p\)-adics are usually \(C_2\) fields.