Rational Places
Abstract
Every rational p-adic absolute value is exactly a finite place of the rational field.
Theorem 1.1 (Rational Places).
Lean statement: D5/S3/Arith/DiophantineApproximation/RationalPlaces.exists_finitePlace_val_eq_padic
Proof. Machine-checked in Lean as D5/S3/Arith/DiophantineApproximation/RationalPlaces.exists_finitePlace_val_eq_padic (✓ std3). ∎
Citation. Ralf Stephan (2026). Subspace-Theorems. URL: https://github.com/rwst/Subspace-Theorems/tree/bfd830f481b296989fa5f0c1e48d9316f72270d8.
Commentary.
Every rational p-adic absolute value is exactly a finite place of the rational field.