The relative class number one problem for function fields, I

Kiran S. Kedlaya

The relative class number one problem for function fields, I

Number Theory 2022-08-26 v3 Algebraic Geometry

Authors: Kiran S. Kedlaya

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.

Keywords

fields class number of quadratic fields algebraic curves

Cite

@article{arxiv.2202.08382,
  title  = {The relative class number one problem for function fields, I},
  author = {Kiran S. Kedlaya},
  journal= {arXiv preprint arXiv:2202.08382},
  year   = {2022}
}

Comments

18 pages, including 3 pages of tables; associated code available at https://github.com/kedlaya/same-class-number/; v3: final version

The relative class number one problem for function fields, I

Abstract

Keywords

Cite

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