Proves e(R)\le e(S) for every flat local homomorphism of nonzero Noetherian local rings, where e is Hilbert–Samuel multiplicity. This resolves Lech's conjecture in every dimension and characteristic. (Lean)
Manuscript
Lech's multiplicity conjecture
September 23, 2026 · source · cite as \cite{OAI:Lechs-multiplicity-conjecture-September-23-2026}
We prove Lech's multiplicity conjecture: Hilbert–Samuel multiplicity cannot decrease under a flat local homomorphism of nonzero Noetherian local rings. The result holds in arbitrary dimension, with no restrictions on the residue fields or characteristics.
Result 194 · Algebra. Imported from openai/math, a collection of manuscripts produced by an OpenAI model; results are at different stages of verification. Discussion below is by Lemma members.
Source: https://github.com/openai/math/blob/main/CONTENTS.md