A uniqueness theorem for rational points in projective space

[摘要] This paper proves a uniqueness result of the following type which has an analogy in Nevanlinna theory. Let K be a number held and S a finite set of places of K containing the infinite places. Let L-1,..., L3m+2 be linear forms in m + 1 variables with coefficients in Q which are in general position. Let x(n), y(n) be two infinite sequences in P-m(K) such that at least one of them is non-degenerate and such that L-j(x(n)) not equal 0, L-j(y(n)) not equal 0, and L-j(x(n))/L-j(y(n)) is an S-unit for 1 less than or equal to j less than or equal to 3m + 2. Then there exists an infinite subsequence {n(k)} with x(nk) = y(nk). (C) 2000 Academic Press.

[发布日期] 2000-11-01