Restrict Scalars

Abstract

Restriction of scalars gives a power bound for Arakelov height of a subspace span.

Theorem 1.1 (Restrict Scalars).

Lean statement: D5/S3/Arith/AbsoluteValues/Heights/RestrictScalars.arakelovMulHeight_span_restrictScalars_rpow_le

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

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

Commentary.

Restriction of scalars gives a power bound for Arakelov height of a subspace span.

References

• Truth anchor: D5/S3/Arith/AbsoluteValues/Heights/RestrictScalars.arakelovMulHeight_span_restrictScalars_rpow_le
• Dependency: D5/S3/Arith/AbsoluteValues/Heights/ArakelovHeightExtension