Del Pezzo surfaces over finite fields and their Frobenius traces

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Title:	Del Pezzo surfaces over finite fields and their Frobenius traces
Author:	Banwait, Barinder; Fite Naya, Francesc; Loughran, Daniel
Other authors:	Universitat Politècnica de Catalunya. TN - Grup de Recerca en Teoria de Nombres
Abstract:	Let S be a smooth cubic surface over a finite field q. It is known that #S( q) = 1 + aq + q2 for some a ¿ {-2, -1, 0, 1, 2, 3, 4, 5, 7}. Serre has asked which values of a can arise for a given q. Building on special cases treated by Swinnerton–Dyer, we give a complete answer to this question. We also answer the analogous question for other del Pezzo surfaces, and consider the inverse Galois problem for del Pezzo surfaces over finite fields. Finally we give a corrected version of Manin's and Swinnerton–Dyer's tables on cubic surfaces over finite fields.
Abstract:	Peer Reviewed
Subject(s):	-Àrees temàtiques de la UPC::Matemàtiques i estadística::Àlgebra -Àrees temàtiques de la UPC::Matemàtiques i estadística -Algebraic logic -Algebraic logic -Lògica algebraica -Lògica algebraica -Classificació AMS::03 Mathematical logic and foundations::03B General logic -Classificació AMS::03 Mathematical logic and foundations::03B General logic
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Document type:	Article - Submitted version Article
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