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Serre's positivity conjecture

Source placement record

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

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Source status
Open
Field
Algebra
Record type
Revision-pinned source placement
Verification
Source-index reviewed
Source grade
secondary
Reviewed
2026-07-27T18:04:33.834Z

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Source trail

  1. Wikipedia list subsection — Exact Algebra subsection in the revision-pinned source.
  2. Wikipedia topic article — Background article linked by the source index; follow its references for deeper study.
  3. Pinned source revision 1366281547 — Revision-pinned snapshot from 7/27/2026.