scientific article

zbMath0544.12011MaRDI QIDQ3333147

Kazuya Kato, Shuji Saito

Publication date: 1983

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zbMATH Keywords

algebraic K-theory\(K_ 2\)idèle class groupsproper scheme over \({\mathbb{Z}}\)two dimensional class field theoriestwo- dimensional arithmetic field

Mathematics Subject Classification ID

Class field theory (11R37) Arithmetic ground fields for abelian varieties (14K15) Coverings in algebraic geometry (14E20) (K)-theory of global fields (11R70) Transcendental field extensions (12F20) Algebraic (K)-theory and (L)-theory (category-theoretic aspects) (18F25) Class field theory; (p)-adic formal groups (11S31) (K)-theory of local fields (11S70) Applications of methods of algebraic (K)-theory in algebraic geometry (14C35)

Related Items (11)

Local abelian Kato-Parshin reciprocity law: A survey ⋮ Vanishing cycles, ramification of valuations, and class field theory. (With the collaboration of Takeshi Saito.) ⋮ Class field theory for arithmetic schemes ⋮ Ramification theory of reciprocity sheaves. II: Higher local symbols ⋮ Modulus of a rational map into a commutative algebraic group ⋮ Generalized Albanese varieties for surfaces ⋮ Class field theory, its three main generalisations, and applications ⋮ Generalised Kawada-Satake method for Mackey functors in class field theory ⋮ The two-dimensional Contou-Carrère symbol and reciprocity laws ⋮ Generalized Albanese varieties for surfaces in characteristic \(p>0\) ⋮ Class field theory for open curves over local fields

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