Mathematical Research Letters

Volume 27 (2020)

Number 3

Inverse Galois problem for del Pezzo surfaces over finite fields

Pages: 845 – 853



Daniel Loughran (Department of Mathematical Sciences, University of Bath, United Kingdom)

Andrey Trepalin (Steklov Mathematical Institute of Russian Academy of Sciences, Moscow, Russia; and National Research University Higher School of Economics, Laboratory of Algebraic Geometry, Moscow, Russia)


We completely solve the inverse Galois problem for del Pezzo surfaces of degree $2$ and $3$ over all finite fields.

Dedicated to the memory of Sir Henry Peter Francis Swinnerton-Dyer.

Received 23 November 2018

Accepted 18 February 2019

Published 20 August 2020