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Tytuł:
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POINTS OF SMALL HEIGHT ON AFFINE VARIETIES DEFINED OVER FUNCTION FIELDS OF FINITE TRANSCENDENCE DEGREE.
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Autorzy:
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GHIOCA, DRAGOS
NGUYEN, DAC-NHAN-TAM
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Temat:
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FINITE fields
EVIDENCE
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Źródło:
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Bulletin of the Australian Mathematical Society; Jun2021, Vol. 103 Issue 3, p418-427, 10p
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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 $\overline {k}$. [ABSTRACT FROM AUTHOR]
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