What Kind of Morphisms Induces Covering Maps over a Real Closed Field?

2025/02/09 by Rizeng Chen, Chen, Rizeng
Computer Science · #14Q30 #Algebraic Geometry (math.AG) #Cellular Automata and Applications #FOS: Computer and information sciences #FOS: Mathematics #Primary 14P10 #Secondary 14A10 #Symbolic Computation (cs.SC)

paper · pdf · doi:10.48550/arxiv.2502.05834

openalex publication_date 2025/02/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this article, we show that a flat morphism of k-varieties (\mathopchar k=0) with locally constant geometric fibers becomes finite étale after reduction. When k is a real closed field, we prove that such a morphism induces a covering map on the rational points.

Related

• Ramified covering maps of singular curves and stability of pulled back bundles
• The étale topos reconstructs varieties over sub-p-adic fields
• Some results from algebraic geometry over Henselian real valued fields
• Weak toroidalization over non-closed fields
• Twisted covers and specializations