Serre's positivity conjecture that if R is a commutative regular local ring, and P, Q are prime ideals of R, then \dim (R/P) + \dim (R/Q) =…

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

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Source: List of unsolved problems in mathematics (CC BY-SA 4.0)