Hasse's norm theorem for \(K_ 2\)

DOI10.1007/BF00962793zbMath0782.12003MaRDI QIDQ5971120

Yoshihiro Koya

Publication date: 7 March 1994

Published in: \(K\)-Theory (Search for Journal in Brave)

zbMATH Keywords

Hasse principlehigher dimensional class field theory\(K_ 2\)-idele class groupidele class complexmodified hypercohomologygeneralized Tate- Nakayama theorem

Mathematics Subject Classification ID

Galois cohomology (12G05) Class field theory (11R37) (K)-theory of global fields (11R70) Grothendieck groups, (K)-theory and commutative rings (13D15) (K_2) and the Brauer group (19C30)

Related Items (2)

Class field theory for a product of curves over a local field ⋮ A generalization of Tate-Nakayama theorem by using hypercohomology

Cites Work

• Hilbert's theorem 90 for \(K^ 2\), with application to the Chow groups of rational surfaces
• \(K_ 2\)-analogs of Hasse's norm theorems
• Class field theory for curves over local fields
• Arithmetic on two dimensional local rings
• A generalization of class formation by using hypercohomology
• The construction of weight-two arithmetic cohomology
• Values of zeta-functions at non-negative integers
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