On S-class number relations of algebraic tori in Galois extensions of global fields

DOI10.1017/S0027763000003809zbMath0754.11034OpenAlexW1519742980MaRDI QIDQ4007699

Masanori Morishita

Publication date: 27 September 1992

Published in: Nagoya Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1017/s0027763000003809

zbMATH Keywords

Grothendieck cohomology\(S\)-class numbersGauss genus formula

Mathematics Subject Classification ID

Étale and other Grothendieck topologies and (co)homologies (14F20) Class field theory (11R37)

Related Items (10)

The Hasse principle for bilinear symmetric forms over a ring of integers of a global function field ⋮ CLASS NUMBERS OF CM ALGEBRAIC TORI, CM ABELIAN VARIETIES AND COMPONENTS OF UNITARY SHIMURA VARIETIES ⋮ On the classification of quadratic forms over an integral domain of a global function field ⋮ A formula for the S-class number of an algebraic torus ⋮ On the flat cohomology of binary norm forms ⋮ Class numbers of multinorm-one tori ⋮ On Tamagawa numbers of CM tori ⋮ On the Hasse norm principle for certain generalized dihedral extensions over \(\mathbb{Q}\) ⋮ A building-theoretic approach to relative Tamagawa numbers of semisimple groups over global function fields ⋮ Cokernels of restriction maps and subgroups of norm one, with applications to quadratic Galois coverings

Cites Work

• Arithmetic and cohomology invariants of semisimple group schemes and compactifications of locally symmetric spaces
• On algebraic tori of norm type
• The class number of cyclotomic function fields
• Rational points in Henselian discrete valuation rings
• On the Tamagawa number of algebraic tori
• Some Remarks to Ono’s theorem on a generalization of Gauss’ genus theory

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