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引用次数: 27
摘要
(1) 本讲座是关于岩泽理论的。在非交换几何学中，场 F1，即一元场（它仍然是一种虚存在），被视为一个重要的对象。岩泽理论的精神接近于 F1 的思想。根据 Z 与 Fq[T ]（Fq 是有限域）的类比，我们在 Z 侧寻找 F̄q[T ] = Fq[T ]⊗Fq F̄q 的类比。与之类似的应该是 Z ⊗F1 F̄1，但这是一种想象的存在。岩泽用∪r≥1Z[ζpr ]（p 是固定素数，ζpr 是一元的原始 p 次根）作为 F̄q[T ] 在 Z 边上的类似物。
(1) This talk is about Iwasawa theory. In non-commutative geometry, the field F1, the field of one element (which is still an imaginary existence), is regarded as an important object. The spirit of Iwasawa theory is near to the idea of F1. In the analogy between Z and Fq[T ] (Fq is a finite field), we look for an analogue of F̄q[T ] = Fq[T ]⊗Fq F̄q on the Z-side. The analogue should be Z ⊗F1 F̄1, but this is an imaginary existence. Iwasawa used ∪r≥1Z[ζpr ] (p is a fixed prime number and ζpr is a primitive p-th root of unity) as an analogue of F̄q[T ] on the Z-side.
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