92 citations · 200 across the 27 of their papers we have counts for
32 papers
Likely and unlikely ramification of algebraic points on curves
Bianca Viray, Isabel Vogt
This paper initiates the study of arithmetic properties of closed points of arbitrary degree on curves. We show that a pointless curve of rank can have only finitely many cycli…
Number fields generated by points in linear systems on curves
Irmak Balçik, Stephanie Chan, Yuan Liu +1
We develop techniques for determining the fibers of a morphism of curves over a nonarchimedean local field . These results have applications to studying closed poin…
Quartic del Pezzo surfaces without quadratic points
Brendan Creutz, Bianca Viray
Previous work of the authors showed that every quartic del Pezzo surface over a number field has index dividing (i.e., has a closed point of degree modulo ),, and asked…
Isolated and parameterized points on curves
Bianca Viray, Isabel Vogt
We give a self-contained introduction to isolated points on curves and their counterpoint, parameterized points, that situates these concepts within the study of the arithmetic of…
Conic bundle threefolds differing by a constant Brauer class and connections to rationality
Sarah Frei, Lena Ji, Soumya Sankar +2
A double cover of ramified over a general -divisor will have the structure of a geometrically standard conic bundle ramified over a sm…
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…