The relative class number one problem for function fields. I

DOI10.1007/s40993-022-00369-yOpenAlexW4302425148WikidataQ125855899 ScholiaQ125855899MaRDI QIDQ2081531

Kiran S. Kedlaya

Publication date: 13 October 2022

Published in: Research in Number Theory (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2202.08382

zbMATH Keywords

function fieldsclass number oneWeil polynomials

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)

Uses Software

• SageMath
• LMFDB
• GitHub

Cites Work

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• Corrigendum to: ``Improved upper bounds for the number of points on curves over finite fields
• A counterexample to `Algebraic function fields with small class number'
• On the Deuring-Shafarevich formula
• Cyclotomic function fields with divisor class number one
• Divisor class number one problem for Abelian extensions over rational function fields
• Algebraic function fields with small class number
• Conjugate algebraic units in a special interval
• Some effective cases of the Brauer-Siegel theorem
• Recovering affine curves over finite fields from \(L\)-functions
• Classification of algebraic function fields with class number one
• Function fields of class number one
• On unique factorization in certain rings of algebraic functions
• Class numbers of cyclotomic function fields
• Algebraic function fields with equal class number
• Curves and Symmetric Spaces, I
• Maps between curves and arithmetic obstructions
• New methods for bounding the number of points on curves over finite fields
• Some analytic estimates of class numbers and discriminants

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