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Frobenius actions on Del Pezzo surfaces of degree 2
Published 23 Nov 2022 in math.AG and math.NT | (2211.12855v1)
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.
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