---
tag: BB7NN8JWEC
kind: conjecture
name: Serre's positivity conjecture
sources:
  - wikipedia: en:183091@r1376385932
    locator: List of unsolved problems in mathematics, section Unsolved problems > Algebra
    note: adopted
    mention: wikipedia://en/183091#2KXK
    sections: [Statement]
inventory: [41EG4W5CKA]
---

## Statement

- Serre's positivity conjecture that if $R$ is a commutative regular local ring, and $P, Q$ are [[prime ideals|00MHHZ9SNE]] of $R$, then $\dim (R/P) + \dim (R/Q) = \dim (R)$ implies $\chi(R/P, R/Q) > 0$.