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Fibered threefolds and Lang-Vojta's conjecture over function fields

Amos Turchet (Institutionen för matematiska vetenskaper, Algebra och geometri)
Transactions of the American Mathematical Society (0002-9947). Vol. 369 (2017), 12, p. 8537-8558.
[Artikel, refereegranskad vetenskaplig]

Using the techniques introduced by Corvaja and Zannier in 2008 we solve the non-split case of the geometric Lang-Vojta Conjecture for affine surfaces isomorphic to the complement of a conic and two lines in the projective plane. In this situation we deal with sections of an affine threefold fibered over a curve, whose boundary, in the natural projective completion, is a quartic bundle over the base whose fibers have three irreducible components. We prove that the image of each section has bounded degree in terms of the Euler characteristic of the base curve.

Nyckelord: Vojta's conjecture, function fields, fibered threefolds, heights, S-units



Denna post skapades 2017-10-31. Senast ändrad 2017-10-31.
CPL Pubid: 252869

 

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Institutioner (Chalmers)

Institutionen för matematiska vetenskaper, Algebra och geometriInstitutionen för matematiska vetenskaper, Algebra och geometri (GU)

Ämnesområden

Matematik

Chalmers infrastruktur