The relative class number one problem for function fields, I

DOI10.1007/S40993-022-00369-YarXiv2202.08382WikidataQ125855899 ScholiaQ125855899MaRDI QIDQ6391351

Kiran S. Kedlaya

Publication date: 16 February 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 $mathbb{F}_2$ and genus $>1$; and give a conjectural answer in the remaining cases. The conjecture will be resolved in subsequent papers.

Mathematics Subject Classification ID

Arithmetic theory of algebraic function fields (11R58) Curves over finite and local fields (11G20) Class numbers, class groups, discriminants (11R29) Algebraic functions and function fields in algebraic geometry (14H05)

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