The Schmidt Subspace Theorem states that the points of small height in projective space satisfying a certain Diophantine approximation condition lie within a finite union of hyperplanes, rather than being spread arbitrarily throughout the space. Proved by Wolfgang M. Schmidt in 1972, it is a far-reaching, multi-dimensional generalization of Roth's Theorem on the approximation of algebraic numbers by rationals, and has become a central tool in Diophantine approximation and its applications to Diophantine equations.
Facts
StatementIf L1,...,Ln are linearly independent linear forms in n variables with algebraic coefficients and epsilon > 0 is any given real number, then the non-zero integer points x with |L1(x)...Ln(x)| < |x|^(-epsilon) lie in a finite number of proper subspaces of Q^n. 1 Classification
Statement Form Connections
Has Statement Form
Entity-backed identity for the statement-form enum value this theorem already carries, resolved to a mathematics concept by an explicit value-to-entity map (phase 3 bucket conversion, docs\design_entity_backed_browse_buckets_20260928.md). The statement-form fact itself stays on the theorem unchanged.
Sources
1. Subspace theorem (Wikipedia)
Statement
lie in a finite number of proper subspaces
Introduction
obtained by Wolfgang M. Schmidt (1972)
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