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Arithmetic Riemann–Roch theorem : ウィキペディア英語版
Arakelov theory
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.
==Background==
Arakelov geometry studies a scheme ''X'' over the ring of integers Z, by putting Hermitian metrics on holomorphic vector bundles over ''X''(C), the complex points of ''X''. This extra Hermitian structure is applied as a substitute, for the failure of the scheme Spec(Z) to be a complete variety.

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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