The class number of hereditary orders in non-Eichler algebras over global function fields

DOI10.1007/BF01460041zbMath0627.16003OpenAlexW2018937833MaRDI QIDQ581511

Marleen Denert, Jan Van Geel

Publication date: 1988

Published in: Mathematische Annalen (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/164469

zbMATH Keywords

global function fieldclass number formulacentral simple algebraEichler conditionhereditary R-orderslocally free left \(\theta \) -idealsnon- Eichler division algebra

Mathematics Subject Classification ID

Arithmetic theory of algebraic function fields (11R58) Finite rings and finite-dimensional associative algebras (16P10) Separable algebras (e.g., quaternion algebras, Azumaya algebras, etc.) (16H05) Quaternion and other division algebras: arithmetic, zeta functions (11R52) Division rings and semisimple Artin rings (16Kxx)

Related Items

On component groups of Jacobians of quaternionic modular curves, Orders in quaternion algebras over global function fields having the cancellation property, Brandt matrices and theta series over global function fields, \(\mathcal D\)-elliptic sheaves and odd Jacobians, Mass formula of division algebras over global function fields, The level of division algebras over local and global fields, Variations of mass formulas for definite division algebras, On Rankin triple product \(L\)-functions over function fields: central critical values, On Jacquet-Langlands isogeny over function fields, Endomorphisms of exceptional \(\mathcal{D}\)-elliptic sheaves, On finite arithmetic simplicial complexes, On finite Drinfeld modules, Local diophantine properties of modular curves of 𝒟-elliptic sheaves

Cites Work

• Orders in quaternion algebras over global function fields having the cancellation property
• Über die Idealklassenzahl total definierter Quaternionenalgebren
• Zur Zahlentheorie der Quaternionen-Algebren.
• Orders, in non-Eichler ($R$)-algebras over global function fields, having the cancellation property.
• Class Groups and Picard Groups of Orders
• Locally free modules over arithmetic orders.
• Type numbers of Eichler orders.
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