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In mathematics, Arakelov theory (or Arakelov geometry) is an approach to Diophantine geometry, named for Suren Arakelov. It is used to study Diophantine equations in higher dimensions.
Results, Background & The arithmetic Riemann–Roch theorem
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| Subject | Predicate | Object | Confidence | Src |
|---|---|---|---|---|
| a Riemann-Roch theorem | instance of | extended Arakelov's work by establishing results | 0.80 | text |
| a Noether formula | instance of | extended Arakelov's work by establishing results | 0.80 | text |
| a Hodge index theorem | instance of | extended Arakelov's work by establishing results | 0.80 | text |
| the nonnegativity of the self-intersection of the dualizing sheaf in this context.Arakelov theory was used by Paul Vojta | instance of | extended Arakelov's work by establishing results | 0.80 | text |
| Arakelov theory | related to References | Arakelov | 0.60 | section |
| Arakelov theory | related to References | Suren | 0.60 | section |
| Arakelov theory | related to References | Intersection | 0.60 | section |
| Arakelov theory | related to References | Math | 0.60 | section |
| Arakelov theory | related to References | USSR Izv | 0.60 | section |
| Arakelov theory | related to References | IM1974v008n06ABEH002141 | 0.60 | section |
| Arakelov theory | related to References | Zbl | 0.60 | section |
| Arakelov theory | related to References | Theory | 0.60 | section |
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