On conjectures of Sharifi
On conjectures of Sharifi
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论谢里菲的猜想
DOI：
10.1215/21562261-2023-0018
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发表时间：
2024
影响因子：
0.6
通讯作者：
Kazuya Kato
中科院分区：
文献类型：
--
作者：
T. Fukaya;Kazuya Kato
(1)这次演讲是关于岩泽理论的。在非交换几何中，域F1，即一个元素的域(它仍然是一个想象的存在)，被认为是一个重要的对象。岩泽理论的精神接近F1的理念。在Z和FQ[T](FQ是有限域)之间的类比中，我们在Z侧寻找F̄Q[T]=FQ[T]⊗FQ F̄Q的类比。类比应该是Z⊗F1 F̄1，但这是一个想象的存在。岩泽使用∪r≥1Z[ζpr](p是固定素数，ζpr是本原p次单位根)作为Z侧的F̄q[T]的类比。
(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.