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Abstract
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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, Fité and Loughran and Loughran and
Trepalin.
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Keywords
Del Pezzo surfaces, moduli spaces, Frobenius endomorphism,
inverse Galois problem, point counts, cohomology
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Mathematical Subject Classification
Primary: 14J10, 14J26
Secondary: 05E18, 14F20
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Milestones
Received: 23 November 2022
Revised: 24 February 2023
Accepted: 19 April 2023
Published: 9 January 2024
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| © 2024 The Author(s), under
exclusive license to MSP (Mathematical Sciences
Publishers). |
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