Class numbers of central simple algebras over global function fields

Fu-Tsun Wei; Chia-Fu Yu

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arXiv · 1208.5612

Class numbers of central simple algebras over global function fields

Fu-Tsun Wei·Chia-Fu Yu

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Abstract

Let $K$ be a global function field together with a place $\infty$, and $A$ the subring of functions regular outside $\infty$. In this paper we present an effective method to evaluate the (locally free) class number of an arbitrary hereditary $A$-order in an arbitrary definite central simple $K$-algebra. We also show that the class number of any non-principal genus for a hereditary order in $D$ can be reduced to that of the principal genus for another hereditary order in $D$.

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Fu-Tsun Wei, Chia-Fu Yu. 2012-08-28. Class numbers of central simple algebras over global function fields. https://arxiv.org/abs/1208.5612

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