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Journals / Hacettepe Journal of Mathematics and Statistics / 2026 / Volume: 50 Issue: 5

Local abelian Kato-Parshin reciprocity law: A survey

Kazim İlhan Ikeda(BOGAZICI UNIVERSITY)0000-0001-6349-3541
Erol Serbest(YEDITEPE UNIVERSITY)0000-0002-3047-0826
Pages
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Publication Date
2021-10-15
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

The paper is geared toward non-abelian generalization of this theory.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:Let $K$ denote an $n$-dimensional local field.
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Key Findings & Data:The aim of this expository paper is to survey the basic arithmetic theory of the $n$-dimensional local field $K$ together with its Milnor $K$-theory and Parshin topological $K$-theory; to review Kato's ramification theory for finite abelian extensions of the $n$-dimensional local field $K$, and to state the local abelian higher-dimensional $K$-theoretic generalization of local abelian class field theory of Hasse, which is developed by Kato and Parshin.
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Conclusion & Impact:The paper is geared toward non-abelian generalization of this theory.
🔬Design:Survey & Empirical Study
📍Scope:Comprehensive Sample
⚙️Variables:higher-dimensional local fields · Milnor K-theory · local class field theory

Abstract

Let $K$ denote an $n$-dimensional local field. The aim of this expository paper is to survey the basic arithmetic theory of the $n$-dimensional local field $K$ together with its Milnor $K$-theory and Parshin topological $K$-theory; to review Kato's ramification theory for finite abelian extensions of the $n$-dimensional local field $K$, and to state the local abelian higher-dimensional $K$-theoretic generalization of local abelian class field theory of Hasse, which is developed by Kato and Parshin. The paper is geared toward non-abelian generalization of this theory.

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Cite This Article

Ikeda, K. İ., Serbest, E. (2021). Local abelian Kato-Parshin reciprocity law: A survey. Hacettepe Journal of Mathematics and Statistics, Volume: 50 Issue: 5. https://doi.org/10.15672/hujms.834042

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