scientific article

zbMath0535.12013MaRDI QIDQ3318871

A. N. Parshin

Publication date: 1984

Title: zbMATH Open Web Interface contents unavailable due to conflicting licenses.

zbMATH Keywords

duality theoryArtin-Schreier dualitiesfundamental almost-isomorphismlocal field of arbitrary dimensionmultidimensional algebraic geometryanalogy of classical class field theorydescription of Abelian extensions in terms of higher K-functors

Mathematics Subject Classification ID

Finite fields and commutative rings (number-theoretic aspects) (11T99) Local ground fields in algebraic geometry (14G20) Brauer groups of schemes (14F22) Algebraic (K)-theory and (L)-theory (category-theoretic aspects) (18F25) Class field theory; (p)-adic formal groups (11S31) (K)-theory of local fields (11S70)

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Abelian local \(p\)-class field theory ⋮ Some elementary remarks about \(n\)-local fields ⋮ Geometric and analytic structures on the higher adèles ⋮ Topology on rational points over \(n\)-local fields ⋮ Convergence sets of multidimensional local fields ⋮ Local abelian Kato-Parshin reciprocity law: A survey ⋮ Explicit form of the Hilbert symbol on polynomial formal module for multidimensional local field. II ⋮ On P-Extensions of Multidimensional Local Fields ⋮ On the properties of the Vostokov and Parshin pairing in higher local class field theory ⋮ Rings generated by convergence sets of multidimensional complete field ⋮ REFINED SWAN CONDUCTORS OF ONE-DIMENSIONAL GALOIS REPRESENTATIONS ⋮ Milnor \(K\)-groups modulo \(p^{n}\) of a complete discrete valuation field ⋮ \(K\)-groups of multidimensional local fields ⋮ Norm series in high-dimensional local fields ⋮ The third homology of \(\mathrm{SL}_2\) of fields with discrete valuation ⋮ Continuous homomorphisms between algebras of iterated Laurent series over a ring ⋮ On the Brauer group of a two-dimensional local field ⋮ Higher-dimensional Contou-Carrère symbol and continuous automorphisms ⋮ The two-dimensional Contou-Carrère symbol and reciprocity laws ⋮ An analog of determinant related to Parshin-Kato theory and integer polytopes ⋮ Locally convex structures on higher local fields ⋮ Shafarevich's paper “A general reciprocity law” ⋮ The unramified two-dimensional Langlands correspondence ⋮ Iterated Laurent series over rings and the Contou-Carrère symbol ⋮ A generalized Contou-Carrère symbol and its reciprocity laws in higher dimensions

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