Abstract
AbstractWe reduce the classification of finite extensions of function fields (of curves over finite fields) with the same class number to a finite computation; complete this computation in all cases except when both curves have base field $$\mathbb {F}_2$$
F
2
and genus $$>1$$
>
1
; and give a conjectural answer in the remaining cases. The conjecture will be resolved in subsequent papers.
Funder
Division of Mathematical Sciences
Publisher
Springer Science and Business Media LLC
Subject
Algebra and Number Theory
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