Weil numbers in finite extensions of ℚ^{𝕒𝕓}: the Loxton-Kedlaya phenomenon

Abstract

A finiteness phenomenon described by Loxton and later by Kedlaya states that, for any fixed m m , there exist (modulo multiplication by roots of unity) only finitely many m m -Weil numbers in Q a b \mathbb {Q}^{ab} . In the present paper we show that this phenomenon extends to all finite extensions of Q a b \mathbb {Q}^{ab} .