Del Pezzo surfaces over finite fields and their Frobenius traces

被引：7

作者：

Banwait, Barinder ^{[1
]}

Fite, Francesc ^{[2
]}

Loughran, Daniel ^{[3
]}

机构：

[1] CMR Surg, Crome Lea Business Pk,Madingley Rd, Cambridge CB23 7PH, England

[2] Univ Politecn Cataluna, Dept Matemat, BGSmath, Edif Omega,C Jordi Girona 1-3, ES-08034 Barcelona, Spain

[3] Univ Manchester, Sch Math, Oxford Rd, Manchester M13 9PL, Lancs, England

来源：

MATHEMATICAL PROCEEDINGS OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY | 2019年 / 167卷 / 01期

基金：

欧洲研究理事会;

关键词：

D O I：

10.1017/S0305004118000166

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let S be a smooth cubic surface over a finite field F-q. It is known that #S(F-q) = 1 + aq + q(2) for some a is an element of{- 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.

引用

页码：35 / 60

页数：26

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