Remarks on endomorphisms and rational points

被引：21

作者：

Amerik, E. ^{[1
]}

Bogomolov, F. ^{[2
,3
]}

Rovinsky, M. ^{[4
,5
]}

机构：

[1] Univ Paris 11, Math Lab, F-91405 Orsay, France

[2] NYU, Courant Inst Math Sci, New York, NY 10012 USA

[3] GU HSE, Lab Algebra Geometry, Moscow 117312, Russia

[4] Independent Univ Moscow, Moscow 119002, Russia

[5] Russian Acad Sci, Inst Informat Transmiss Problems, Moscow 117901, Russia

来源：

COMPOSITIO MATHEMATICA | 2011年 / 147卷 / 06期

关键词：

rational points; rational maps; p-adic neighbourhood; FIBRATIONS; VARIETY; LINES;

D O I：

10.1112/S0010437X11005537

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let X be an algebraic variety and let f : X -> X be a rational self-map with a fixed point q, where everything is defined over a number field K. We make some general remarks concerning the possibility of using the behaviour of f near q to produce many rational points on X. As an application, we give a simplified proof of the potential density of rational points on the variety of lines of a cubic fourfold, originally proved by Claire Voisin and the first author in 2007.

引用

页码：1819 / 1842

页数：24

共 30 条

[1] AMERIK E, 2009, ANN FAC SCI TOULOUSE, V18, P445
[2] Amerik E, 2008, PURE APPL MATH Q, V4, P509
[3] POTENTIAL DENSITY OF RATIONAL POINTS ON THE VARIETY OF LINES OF A CUBIC FOURFOLD
Amerik, Ekaterina
Voisin, Claire
[J]. DUKE MATHEMATICAL JOURNAL, 2008, 145 (02) : 379 - 408
[4] Arnold V.I., 1988, GRUNDLEHREN MATH WIS, V250
[5] Atiyah M. F., 1969, Introduction to Commutative Algebra
[6] BEAUVILLE A, 1985, CR ACAD SCI I-MATH, V301, P703
[7] Beauville A., 1983, Progr. Math., V39, P1
[8] Bogomolov F. A., 2000, ASIAN J MATH, V4, P351, DOI 10.4310/AJM.2000.v4.n2.a6
[9] Campana F, 2004, ANN I FOURIER, V54, P499, DOI 10.5802/aif.2027
[10] Chen X., ARXIVMATH10081619

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