POINTS OF SMALL HEIGHT ON AFFINE VARIETIES DEFINED OVER FUNCTION FIELDS OF FINITE TRANSCENDENCE DEGREE
| Autor: | Dac-Nhan-Tam Nguyen, Dragos Ghioca |
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| Rok vydání: | 2020 |
| Předmět: |
Pure mathematics
Subvariety General Mathematics 010102 general mathematics Field (mathematics) 010103 numerical & computational mathematics Transcendence degree Function (mathematics) 01 natural sciences Bogomolov conjecture Direct proof Affine transformation 0101 mathematics Function field Mathematics |
| Zdroj: | Bulletin of the Australian Mathematical Society. 103:418-427 |
| ISSN: | 1755-1633 0004-9727 |
| Popis: | We provide a direct proof of a Bogomolov-type statement for affine varieties V defined over function fields K of finite transcendence degree over an arbitrary field k, generalising a previous result (obtained through a different approach) of the first author in the special case when K is a function field of transcendence degree $1$ . Furthermore, we obtain sharp lower bounds for the Weil height of the points in $V(\overline {K})$ , which are not contained in the largest subvariety $W\subseteq V$ defined over the constant field $\overline {k}$ . |
| Databáze: | OpenAIRE |
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