Algebras of linear growth and the dynamical Mordell–Lang conjecture
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DOI: 10.1016/j.aim.2018.11.016
Abstract: Ufnarovski remarked in 1990 that it is unknown whether any finitely presented associative algebra of linear growth is automaton, that is, whether the set of normal words in the algebra form a regular language. If… read more here.
Keywords: growth; lang conjecture; mordell lang; dynamical mordell ... See more keywords
A SPARSITY RESULT FOR THE DYNAMICAL MORDELL–LANG CONJECTURE IN POSITIVE CHARACTERISTIC
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DOI: 10.1017/s0004972721000083
Abstract: Abstract We prove a quantitative partial result in support of the dynamical Mordell–Lang conjecture (also known as the DML conjecture) in positive characteristic. More precisely, we show the following: given a field K of characteristic… read more here.
Keywords: lang conjecture; mordell lang; dynamical mordell; conjecture positive ... See more keywords
Growth rate of ample heights and the Dynamical Mordell–Lang conjecture
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DOI: 10.1142/s1793042118501610
Abstract: We provide an explicit formula on the growth rate of ample heights of rational points under iteration of endomorphisms of smooth projective varieties over number fields. As an application, we give a positive answer to… read more here.
Keywords: rate ample; dynamical mordell; ample heights; growth rate ... See more keywords