The distribution of class groups of function fields

By Jeff Achter. 2004

57 citations recorded by the source corpus.

Abstract For any sufficiently general family of curves over a finite field F q and any elementary abelian l -group H with l relatively prime to q, we give an explicit formula for the proportion of curves C for which Jac ( C ) [ l ] ( F q ) ≅ H . In doing so, we prove a conjecture of Friedman and Washington.

Subfields: Artificial Intelligence, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/c2d542952d6303007df6cef316d57e5a8ba80912

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Artificial Intelligence

1. Chris Hall
2. R. Pries

In Geometry and Topology

1. Chris Hall
2. R. Pries
3. Jeff Achter
4. Igor E. Shparlinski

In Mathematical Physics

1. Chris Hall
2. R. Pries

Citations in the corpus

• Big symplectic or orthogonal monodromy modulo $\ell$ (2006, methodology): “Achter applied Yu’s theorem in [ Ac ] to prove a conjecture of Friedman and Washington on class groups of quadratic function fields.”
• The integral monodromy of hyperelliptic and trielliptic curves (2006, background): “The moduli spaces M̃G andMG are smooth, proper Deligne-Mumford stacks over SpecZ[1/d,ζd].”