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Riemann–Roch theorem

theorem that the Euler characteristic of the sheaf cohomology of a holomorphic line bundle on a Riemann surface equals the degree of the bundle plus half of the Euler characteristic of the surface
Intangible theorem Q379048
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Riemann–Roch theorem

Summary

Riemann–Roch theorem is a theorem[1]. It draws 81 Wikipedia views per month (theorem category, ranking #197 of 1,306).[2]

Key Facts

  • Riemann–Roch theorem's instance of is recorded as theorem[3].
  • Bernhard Riemann is named after Riemann–Roch theorem[4].
  • Gustav Roch is named after Riemann–Roch theorem[5].
  • Riemann–Roch theorem's part of is recorded as list of theorems[6].
  • Riemann–Roch theorem's Freebase ID is recorded as /m/01krvf[7].
  • Riemann–Roch theorem's proved by is recorded as Gustav Roch[8].
  • Riemann–Roch theorem's statement describes is recorded as compact Riemann surface[9].
  • Riemann–Roch theorem's defining formula is recorded as \dim\operatorname H^0(\Sigma,L)-\dim\operatorname H^1(\Sigma,L)=\deg(L)+1-g(\Sigma)[10].
  • Riemann–Roch theorem's studied by is recorded as algebraic geometry[11].
  • Riemann–Roch theorem's maintained by WikiProject is recorded as WikiProject Mathematics[12].
  • Riemann–Roch theorem's Microsoft Academic ID is recorded as 2777639948[13].
  • Riemann–Roch theorem's ProofWiki ID is recorded as Riemann-Roch_Theorem[14].
  • Riemann–Roch theorem's in defining formula is recorded as \Sigma[15].
  • Riemann–Roch theorem's in defining formula is recorded as L[16].
  • Riemann–Roch theorem's in defining formula is recorded as g[17].
  • Riemann–Roch theorem's in defining formula is recorded as \deg[18].
  • Riemann–Roch theorem's in defining formula is recorded as \operatorname H[19].
  • Riemann–Roch theorem's in defining formula is recorded as \dim[20].
  • Riemann–Roch theorem's ScienceDirect topic ID is recorded as mathematics/riemann-roch-theorem[21].

Why It Matters

Riemann–Roch theorem draws 81 Wikipedia views per month (theorem category, ranking #197 of 1,306).[2] It has Wikipedia articles in 12 language editions, a strong signal of global cultural recognition.[22]

Related Entities

Bernhard Riemann

References

Programmatic citations — every numbered marker resolves to a verifiable graph row below.

Direct Wikidata claims

  1. [3] ↑ . wikidata.org.
  2. [4] ↑ . wikidata.org.
  3. [5] ↑ . wikidata.org.
  4. [6] ↑ . wikidata.org.
  5. [7] ↑ . Freebase Data Dumps. wikidata.org.
  6. [8] ↑ . wikidata.org.
  7. [9] ↑ . wikidata.org.
  8. [10] ↑ . wikidata.org.
  9. [11] ↑ . wikidata.org.
  10. [12] ↑ . wikidata.org.
  11. [13] ↑ . wikidata.org.
  12. [14] ↑ . wikidata.org.
  13. [15] ↑ . wikidata.org.
  14. [16] ↑ . wikidata.org.
  15. [17] ↑ . wikidata.org.
  16. [18] ↑ . wikidata.org.
  17. [19] ↑ . wikidata.org.
  18. [20] ↑ . wikidata.org.
  19. [21] ↑ . wikidata.org.

Class ancestry

  1. [1] ↑ . Wikidata. wikidata.org.

Aggregate / graph-position facts

  1. [2] ↑ . Wikimedia Foundation. dumps.wikimedia.org.
  2. [22] ↑ . Wikidata sitelinks. wikidata.org.

📑 Cite this page

Use these citations when quoting this entity in research, articles, AI prompts, or wherever provenance matters. We aggregate Wikidata + Wikipedia + authoritative open-data sources; the stitched, scored, cross-referenced view is what 4ort.xyz contributes.

APA 4ort.xyz Knowledge Graph. (2026). Riemann–Roch theorem. Retrieved May 3, 2026, from https://4ort.xyz/entity/riemann-roch-theorem
MLA “Riemann–Roch theorem.” 4ort.xyz Knowledge Graph, 4ort.xyz, 3 May. 2026, https://4ort.xyz/entity/riemann-roch-theorem.
BibTeX @misc{4ortxyz_riemann-roch-theorem_2026, author = {{4ort.xyz Knowledge Graph}}, title = {{Riemann–Roch theorem}}, year = {2026}, url = {https://4ort.xyz/entity/riemann-roch-theorem}, note = {Accessed: 2026-05-03}}
LLM prompt According to 4ort.xyz Knowledge Graph (aggregator of Wikidata, Wikipedia, and authoritative open-data sources): Riemann–Roch theorem — https://4ort.xyz/entity/riemann-roch-theorem (retrieved 2026-05-03)

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