LangVojta conjecture and smooth hypersurfaces over number fields
Ariyan Javanpeykar (Mainz)
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When 
May 12, 2016 from 10:30 am to 11:30 am 
Where  Bonn, HĂ¶rsaal MPI, Vivatsgasse 7 
Contact Name  sachinidis 
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Siegel proved the finiteness of the number of solutions to the unit equation in a number ring, i.e., for a number field K with ring of integers O, the equation x+y = 1 has only finitely many solutions in O*. That is, reformulated in more algebrogeometric terms, the hyperbolic curve P^1{0,1,infty} has only finitely many "integral points". In 1983, Faltings proved the Mordell conjecture generalizing Siegel's theorem: a hyperbolic complex algebraic curve has only finitely many integral points. Inspired by Faltings's and Siegel's finiteness results, Lang and Vojta formulated a general finiteness conjecture for "integral points" on complex algebraic varieties: a hyperbolic complex algebraic variety has only finitely many "integral points" . In this talk we will explain the LangVojta conjecture and we will explain some of its consequences for the arithmetic of homogeneous polynomials over number fields. This is joint work with Daniel Loughran.