Genus Stability of \mathbb Z_p^×-Towers

2025/07/18 by Wang, Shiruo
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2507.14247

Abstract

Let p be a prime. Consider a tower of smooth projective geometrically irreducible curves over \mathbb F_p, \mathscr C:⋯→ C_n→⋯→ C₁→ C₀=\mathbb P¹ whose Galois group is isomorphic to \mathbb Z_p^×. In this paper, we study genus growth of the tower \mathscr C and determine all the \mathbb Z_p^×-towers with genus be a quadratic equation of pⁿ when n is sufficiently large.

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