Frobenius actions on Del Pezzo surfaces of degree 2
Algebraic Geometry
2024-01-10 v1 Number Theory
Abstract
We determine the number of Del Pezzo surfaces of degree 2 over finite fields of odd characteristic with specified action of the Frobenius endomorphism, i.e. we solve the "quantitative inverse Galois problem". As applications we determine the number of Del Pezzo surfaces of degree 2 with a given number of points and recover results of Banwait-Fit\'e-Loughran and Loughran-Trepalin.
Keywords
Cite
@article{arxiv.2211.12855,
title = {Frobenius actions on Del Pezzo surfaces of degree 2},
author = {Olof Bergvall},
journal= {arXiv preprint arXiv:2211.12855},
year = {2024}
}
Comments
9 pages, 2 tables, comments welcome