The relative class number one problem for function fields, I
Kiran S. Kedlaya · Research in Number Theory · 2022
Abstract We 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.