MathDBWeak Lang conjecture for varieties of general type
Weak Lang conjecture for varieties of general type
Let be a smooth variety of general type defined over a number field.
Weak Lang conjecture. Rational points on are not potentially dense.
The conjecture is stated as the logical negation of the two potential-density conjectures above. It is proved only for curves and subvarieties of abelian varieties, and remains open in general.
Sources & referencesView supporting material
Primary source
Ivan Cheltsov, “Birationally superrigid cyclic triple spaces”, arXiv:math/0410558 (2004).
Additional references
3 papers in this index state this conjecture (1998–2004). The statement above is taken from the most recent of them; the others are arXiv:math/0311465, arXiv:math/9809015.
Progress summary
Nothing recorded yet. Refresh searches the literature and the public web for attempts on this problem, and writes the first summary here.
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