Source label: Unsolved
Source status date unavailable · Observed Oct 1, 2026
The cited source item and version only; this is not an independent OpenMath assessment.
Algebraic geometry MSC2020 14C30
conjectureHodge conjecture
OpenGeneral case unresolved
The general statement is reported open by Clay; proved special cases have not been curated here.
Source report · observed Oct 1, 2026
Viewing pinned publication v2. View the current publication →
Question & scope
On a smooth complex projective variety, is every rational Hodge class a rational linear combination of classes of algebraic cycles?
The rational Hodge conjecture; integral variants are different statements.
Question paraphrased by OpenMath. Use the cited source and locator for authoritative wording.
Research state
OpenGeneral case unresolved
The general statement is reported open by Clay; proved special cases have not been curated here.
Still unresolved: The general statement remains unresolved according to the cited source. Partial-result coverage is not assessed here.
Source report · observed Oct 1, 2026 · Clay · Millennium Problems
This is a discovery entry. OpenMath has checked the linked source and attribution; it has not independently assessed the present mathematical status.
Literature & sources
Clay problem page and official description ↗
Source state checked on 1 October 2026. The page does not provide a status-update date; current literature has not been independently reviewed.
Provenance & coverage
Published after staff preview and source checks. This page covers the cited items; it does not represent a complete list of problems or a literature-wide review.
- No exhaustive literature or source-list coverage.
- Independent mathematical assessment has not been performed.
Clay · Millennium Problems ↗
Clay Mathematics Institute · metadata-link · Not established; links and OpenMath paraphrases only
Store metadata and original OpenMath paraphrases; follow the original source for authoritative wording. Rights / source terms
1 cited entry · exact source identity
- Version
- clay-millennium@observed-2026-10-01
- Revision
- observed-2026-10-01
- Content SHA-256
- No upstream byte snapshot retained; linked metadata only
- Source update
- Unavailable
- Observed
- 2026-10-01
- Check cadence
- 30 days
- https://www.claymath.org/millennium/hodge-conjecture/ ↗
hodge-conjecture:entry:0:v1
Publication v2 · history & checksums
- Stable Problem ID
- problem-hodge-conjecture
- Publication SHA-256
- 1be285c6bd00ce06475f059615a54bc1e95f7b6f21ae2e13031cd74c95f6687f
- Published
- 2026-10-10T06:01:24.736315+00:00
- Publication reason
- Add cited resolution scope and consolidate equivalent prime formulations and supporting Claims; mathematical evidence and execution review remain distinct.
- v1 · publish · Sep 30, 2026
Initial checked pilot publication; source attribution, rights, wording and coverage reviewed by OpenMath staff.
- v2 · publish · Oct 10, 2026
Add cited resolution scope and consolidate equivalent prime formulations and supporting Claims; mathematical evidence and execution review remain distinct.
- v3 · publish · Oct 10, 2026
Publish checked pilot curation with canonical Claims and scoped progress; preserve exact source revisions, assumptions, coverage limits and historical publications. External artifacts and OpenMath execution remain distinct.
- v4 · publish · Oct 10, 2026
Publish checked pilot curation with canonical Claims and scoped progress; preserve exact source revisions, assumptions, coverage limits and historical publications. External artifacts and OpenMath execution remain distinct.
- v5 · publish · Oct 10, 2026
Publish checked pilot curation with canonical Claims and scoped progress; preserve exact source revisions, assumptions, coverage limits and historical publications. External artifacts and OpenMath execution remain distinct.
- v6 · publish · Oct 11, 2026
Publish checked pilot curation with canonical Claims and scoped progress; preserve exact source revisions, assumptions, coverage limits and historical publications. External artifacts and OpenMath execution remain distinct.
- v7 · publish · Oct 11, 2026
Publish checked pilot curation with canonical Claims and scoped progress; preserve exact source revisions, assumptions, coverage limits and historical publications. External artifacts and OpenMath execution remain distinct.
- v8 · publish · Oct 11, 2026
Publish checked pilot curation with canonical Claims and scoped progress; preserve exact source revisions, assumptions, coverage limits and historical publications. External artifacts and OpenMath execution remain distinct.
- v9 · publish · Oct 11, 2026
Publish checked pilot curation with canonical Claims and scoped progress; preserve exact source revisions, assumptions, coverage limits and historical publications. External artifacts and OpenMath execution remain distinct.
- v10 · publish · Oct 11, 2026
Reviewed reader correction: preserve assertion history, exact citations and scoped assessments; task evidence names its exact Claim target.
- v11 · publish · Oct 12, 2026
Reviewed reader correction: preserve assertion history, exact citations and scoped assessments; task evidence names its exact Claim target.
- v12 · publish · Oct 13, 2026
Reviewed reader correction: preserve assertion history, exact citations and scoped assessments; task evidence names its exact Claim target.
- v13 · publish · Oct 13, 2026
Reviewed reader correction: preserve assertion history, exact citations and scoped assessments; task evidence names its exact Claim target.
- v14 · publish · Oct 15, 2026
Reviewed reader correction: preserve assertion history, exact citations and scoped assessments; task evidence names its exact Claim target.
- v15 · publish · Oct 15, 2026
Reviewed reader correction: preserve assertion history, exact citations and scoped assessments; task evidence names its exact Claim target.