3 citations · 16 across the 21 of their papers we have counts for
14 papers · 1 filter
On the Chevalley-Bass number of a field
Jean Gillibert, Florence Gillibert, Gabriele Ranieri
We give upper and lower bounds on the Chevalley-Bass number of a field of characteristic zero, whenever this quantity is well-defined. We also describe an algorithm which computes…
Counting rational points on elliptic and hyperelliptic curves over function fields
Jean Gillibert, Emmanuel Hallouin, Aaron Levin
Combining -descent techniques with Riemann-Roch and Bézout's theorems, we give an upper bound on the number of rational points of bounded height on elliptic and hyperelliptic cu…
Arithmetic rank bounds for abelian varieties over function fields
Félix Baril Boudreau, Jean Gillibert, Aaron Levin
It follows from the Grothendieck-Ogg-Shafarevich formula that the rank of an abelian variety (with trivial trace) defined over the function field of a curve is bounded by a quantit…
Galois covers of and number fields with large class groups
Jean Gillibert, Pierre Gillibert
For each finite subgroup of , and for each integer coprime to , we construct explicitly infinitely many Galois extensions of with group $…
Unramified Heisenberg group extensions of number fields
Frauke Bleher, Ted Chinburg, Jean Gillibert
We construct étale generalized Heisenberg group covers of hyperelliptic curves over number fields. We use these to produce infinite families of quadratic extensions of cyclotomic f…
Elliptic surfaces over and large class groups of number fields
Jean Gillibert, Aaron Levin
Given a non-isotrivial elliptic curve over with large Mordell-Weil rank, we explain how one can build, for suitable small primes , infinitely many fields of degr…