Arakelov Height Extension

Abstract

Arakelov tuple height grows by the extension degree under scalar extension.

Theorem 1.1 (Arakelov Height Extension).

Lean statement: D5/S3/Arith/AbsoluteValues/Heights/ArakelovHeightExtension.arakelovMulHeight_pow_finrank

Proof. Machine-checked in Lean as D5/S3/Arith/AbsoluteValues/Heights/ArakelovHeightExtension.arakelovMulHeight_pow_finrank (✓ std3). ∎

Citation. Ralf Stephan (2026). Subspace-Theorems. URL: https://github.com/rwst/Subspace-Theorems/tree/bfd830f481b296989fa5f0c1e48d9316f72270d8.

Commentary.

Arakelov tuple height over a number-field extension is the base-field height raised to the extension degree.

References

• Truth anchor: D5/S3/Arith/AbsoluteValues/Heights/ArakelovHeightExtension.arakelovMulHeight_pow_finrank
• Dependency: D5/S3/Arith/AbsoluteValues/Heights/RowEntryHeight