22 citations · 39 across the 4 of their papers we have counts for
5 papers
Orbits of automorphism groups of fields
Kiran S. Kedlaya, Bjorn Poonen
We address several specific aspects of the following general question: can a field K have so many automorphisms that the action of the automorphism group on the elements of K has r…
The conjugate dimension of algebraic numbers
Neil Berry, Arturas Dubickas, Noam D. Elkies +2
We find sharp upper and lower bounds for the degree of an algebraic number in terms of the -dimension of the space spanned by its conjugates. For all but seven nonnegative integ…
Finiteness results for modular curves of genus at least 2
Matthew Baker, Enrique Gonzalez-Jimenez, Josep Gonzalez +1
A curve X over the field Q of rational numbers is modular if it is dominated by X_1(N) for some N; if in addition the image of its jacobian in J_1(N) is contained in the new subvar…
Curves of every genus with many points, II: Asymptotically good families
Noam D. Elkies, Everett W. Howe, Andrew Kresch +3
We resolve a 1983 question of Serre by constructing curves with many points of every genus over every finite field. More precisely, we show that for every prime power q there is a…
Large torsion subgroups of split Jacobians of curves of genus two or three
Everett W. Howe, Franck Leprevost, Bjorn Poonen
We construct examples of families of curves of genus 2 or 3 over Q whose Jacobians split completely and have various large rational torsion subgroups. For example, the rational poi…