Class numbers of central simple algebras over global function fields
Fu-Tsun Wei, Chia-Fu Yu

TL;DR
This paper introduces an effective method to compute class numbers of hereditary orders in central simple algebras over global function fields, simplifying calculations across different genera.
Contribution
It provides a new computational approach for class numbers and reduces complex genus calculations to simpler principal genus cases.
Findings
Method for evaluating class numbers of hereditary orders
Reduction of non-principal genus class numbers to principal genus
Applicable to arbitrary definite central simple algebras
Abstract
Let be a global function field together with a place , and the subring of functions regular outside . In this paper we present an effective method to evaluate the (locally free) class number of an arbitrary hereditary -order in an arbitrary definite central simple -algebra. We also show that the class number of any non-principal genus for a hereditary order in can be reduced to that of the principal genus for another hereditary order in .
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Taxonomy
TopicsAdvanced Topics in Algebra · Algebraic Geometry and Number Theory · Algebraic structures and combinatorial models
