Number Field Integral Lattice

Abstract

Integral points of a subspace have unit Pluecker ideal in the primitive normalization.

Theorem 1.1 (Number Field Integral Lattice).

Lean statement: D5/S3/Arith/AbsoluteValues/Heights/NumberFieldIntegralLattice.prod_mul_plucker_eq_one

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

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

Commentary.

Integral points of a subspace have unit Pluecker ideal in the primitive normalization.

References

• Truth anchor: D5/S3/Arith/AbsoluteValues/Heights/NumberFieldIntegralLattice.prod_mul_plucker_eq_one
• Dependency: D5/S3/Arith/AbsoluteValues/Heights/Duality
• Dependency: D5/S3/Arith/AbsoluteValues/Heights/MixedLattice
• Dependency: D5/S3/Arith/AbsoluteValues/Heights/PseudoBasis