The distribution of class groups of function fields

Abstract

Using equidistribution results of Katz and a computation in finite symplectic groups, we give an explicit asymptotic formula for the proportion of curves C over a finite field for which the l-torsion of Jac(C) is isomorphic to a given abelian l-group. In doing so, we prove a conjecture of Friedman and Washington

To appear, JPAA

Cited by in corpus (19)

• The integral monodromy of hyperelliptic and trielliptic curves
• Nonabelian Cohen-Lenstra Moments
• Random matrices, the Cohen-Lenstra heuristics, and roots of unity
• Limits and fluctuations of $p$-adic random matrix products
• The p-rank strata of the moduli space of hyperelliptic curves
• Groups from Cyclic Infrastructures and Pohlig-Hellman in Certain Infrastructures
• Joint distribution of the cokernels of random $p$-adic matrices
• Sums of Euler products and statistics of elliptic curves
• The geometric average size of Selmer groups over function fields
• A predicted distribution for Galois groups of maximal unramified extensions
• Monodromy of the p-rank strata of the moduli space of curves
• Cohen-Lenstra heuristics and bilinear pairings in the presence of roots of unity
• Cohen Lenstra Heuristics for Étale Group Schemes and Symplectic Pairings
• Statistics of the Jacobians of hyperelliptic curves over finite fields
• On the distribution of class groups of number fields
• Presentations of Galois groups of maximal extensions with restricted ramification
• Monogenicity and 2-torsion in the class group of number fields of odd degree
• Divisibility of function field class numbers
• Class Number and Regulator Computation in Purely Cubic Function Fields of Unit Rank Two