179 citations · 1.4k across the 75 of their papers we have counts for
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The Mathieu group is a Galois group over
Xiaoyu Huang, Blake Jackson, Kyu-Hwan Lee +3
Researchers studying the inverse Galois problem realized 25 of the 26 sporadic finite simple groups as Galois groups over during 1984-1989. We complete this program by…
Brauer-Manin obstructions requiring arbitrarily many Brauer classes
Jennifer Berg, Carlo Pagano, Bjorn Poonen +4
On a projective variety defined over a global field, any Brauer--Manin obstruction to the existence of rational points is captured by a finite subgroup of the Brauer group. We show…
Abelian varieties of prescribed order over finite fields
Raymond van Bommel, Edgar Costa, Wanlin Li +2
Given a prime power and , we prove that every integer in a large subinterval of the Hasse--Weil interval is $#A(\mathbb{F}_q)$…
A -adic approach to rational points on curves
Bjorn Poonen
In 1922, Mordell conjectured the striking statement that for a polynomial equation , if the topology of the set of complex number solutions is complicated enough, then th…
The local-global principle for integral points on stacky curves
Manjul Bhargava, Bjorn Poonen
We construct a stacky curve of genus (i.e., Euler characteristic ) over that has an -point and a -point for every prime but no $…
Linear independence in linear systems on elliptic curves
Bradley W. Brock, Bruce W. Jordan, Bjorn Poonen +2
Let be an elliptic curve, with identity , and let be a cyclic subgroup of odd order , over an algebraically closed field with . For…