اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدSome cases of Vojtas conjectures related to algebraic tori over function fields
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We first formulate a function field version of Vojtas generalized abc conjecture for algebraic tori. We then show a function field analogue of the Lang-Vojta Conjecture for varieties of log general type that are ramified covers of $mathbb G_m^n$. In particular, it includes the case $ mathbb P^nsetminus D$, where $D$ is a hypersurface over a function field in $mathbb P^n$ with $n+1$ irreducible components and $deg Dge n+2$. The main tools include generalizations of the techniques developed by Corvaja and Zannier in 2008 and 2013 and a gcd estimate of two multivariable polynomials over function fields evaluated at $S$-unit arguments. The gcd theorem obtained here is an adaptation of Levins methods for number fields in 2019 via a weaker version of Schmidts subspace theorem over function fields, which we derive with the use of Vojtas machine in a setting over the constant fields.
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