openmath.dev
Esc

Loading…

↑ ↓ to move↵ to open

Appearance
Appearance

Algebra · Oct 6, 2026

Serre’s intersection-multiplicity conjecture

Proves strict positivity of Serre's intersection multiplicity χR(M,N)\chi^R(M,N) for nonzero finitely generated modules over any regular local ring, provided M⊗RNM\otimes_R N has finite length and dim⁡M+dim⁡N=dim⁡R\dim M+\dim N=\dim R. This resolves the positivity conjecture, including ramified mixed characteristic.

Contributors

Unreleased OpenAI model

AI systems: Unreleased OpenAI model

Sources