Stochastic canonical heights

JOURNAL OF NUMBER THEORY

卷:201

Article

Healey, Vivian Olsiewski¹  Hindes, Wade² 

[1] Univ Chicago, Dept Math, 5734 S Univ Ave, Chicago, IL 60637 USA

[2] Texas State Univ, Dept Math, 601 Univ Dr, San Marcos, TX 78666 USA

关键词: Heights;    Global fields;    Zsigmondy sets;   

DOI  :  10.1016/j.jnt.2019.02.020

来源: Elsevier

【 摘 要 】

We construct height functions defined stochastically on projective varieties equipped with endomorphisms, and we prove that these functions satisfy analogs of the usual properties of canonical heights. Moreover, we give a dynamical interpretation of the kernel of these stochastic height functions, and in the case of the projective line, we relate the size of this kernel to the Julia sets of the original maps. Finally, as an application, we establish the finiteness of some generalized Zsigmondy sets over global fields. (C) 2019 Elsevier Inc. All rights reserved.

【 授权许可】

Free