Integral points, divisibility between values of polynomials and entire curves on surfaces

Details Integral points, divisibility between values of polynomials and entire curves on surfaces Integral points, divisibility between values of polynomials and entire curves on surfaces

2009-07-09

arxiv.org/abs/0907.1517v2

Mathematics

Number Theory

minor changes, two references added

Scientific paper

We prove some new degeneracy results for integral points and entire curves on surfaces; in particular, we provide the first example, to our knowledge, of a simply connected smooth variety whose sets of integral points are never Zariski-dense (and no entire curve has Zariski-dense image). Some of our results are connected with divisibility problems, i.e. the problem of describing the integral points in the plane where the values of some given polynomials in two variables divide the values of other given polynomials.

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