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- W3014597761 abstract "We study the finiteness, growth order, generic emptyness, and uniformity of the set of (S,D)-integral sections in an abelian fibration A over a compact Riemann surface B. Here, S is an arbitrary subset of B and not necessarily finite. These integral sections correspond to rational points of the generic fibre of A and which intersect the divisor D only possibly above S. We introduce in this context the so-called hyperbolic-homotopic height as a substitute for the classical intersection theory. We then establish several new results concerning the finiteness of various large unions of (S,D)-integral points and their polynomial growth in terms of the caradinality of the restriction of S in U, where the sets S is required to be finite only in a certain small open subset U of B. Such results are out of reach of a purely algebraic method. Thereby, we give some new evidence and phenomena to the Geometric Lang-Vojta conjecture. When A is an elliptic surface, we obtain the same results for certain unions of (S,D)-integral points, where both S and D are allowed to vary in certain families. A negative finiteness result concerning the Parshin-Arakelov theorem is also given." @default.
- W3014597761 created "2020-04-10" @default.
- W3014597761 creator A5021807415 @default.
- W3014597761 date "2020-03-06" @default.
- W3014597761 modified "2023-09-27" @default.
- W3014597761 title "Generalized integral points on abelian varieties" @default.
- W3014597761 hasPublicationYear "2020" @default.
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