Local abelian Kato-Parshin reciprocity law: A survey
Hacettepe Journal of Mathematics and Statistics, cilt.50, sa.5, ss.1225-1250, 2021 (SCI-Expanded, Scopus, TRDizin)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 50 Sayı: 5
- Basım Tarihi: 2021
- Doi Numarası: 10.15672/hujms.834042
- Dergi Adı: Hacettepe Journal of Mathematics and Statistics
- Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, zbMATH, TR DİZİN (ULAKBİM)
- Sayfa Sayıları: ss.1225-1250
- Anahtar Kelimeler: Higher-dimensional local fields, Local class field theory, Milnor K-theory
- Açık Arşiv Koleksiyonu: AVESİS Açık Erişim Koleksiyonu
- Boğaziçi Üniversitesi Adresli: Evet
Özet
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.