Abstract:

Creutz and Viray have recently proven the existence of quartic del Pezzo surfaces over the field Q which do not admit a quadratic point, despite every such surface admitting a quadratic point over any local field. In this talk, we will provide an overview of what is known about this problem for other fields and prove the analogous result over global function fields. This is joint work with Giorgio Navone, Katerina Santicola and Haowen Zhang.