Vojta's conjecture and arithmetic dynamics
Speaker: Yohsuke Matsuzawa (Brown University)

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Meeting ID: 947 8793 7855
Passcode: 323472

Time: 9h15, Friday, January 8, 2021

Abstract: I will discuss applications of Vojta's conjecture to some problems in arithmetic dynamics, concerning the growth of sizes of coordinates of orbits, greatest common divisors among coordinates, and prime factors of coordinates. These problems can be restated and generalized in terms of (local/global) height functions, and I proved estimates on asymptotic behavior of height functions along orbits assuming Vojta's conjecture.

One of the key inputs is an asymptotic estimate of log canonical thresholds of (X, f^{-n}(Y)), where f : X->X is a self-morphism and Y is a closed subscheme of X.

As corollaries, I showed that Vojta's conjecture implies Dynamical Lang-Siegel conjecture for projective spaces (the sizes of coordinates grow in the same speed),and existence of primitive prime divisors in higher dimensional setting.

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