Vojta's main conjecture on some rational varieties


10:10 - 11:00

101 , Mathematics Research Center Building (ori. New Math. Bldg.)

Vojta's Main Conjecture is a very deep conjecture in Diophantine geometry. It is a height inequality for rational points on projective varieties, and it suggests a way the global geometry of the variety controls the arithmetic. Many cases of the conjecture still remain unconfirmed. In this talk, we will discuss the conjecture for some rational varieties and its applications to arithmetic dynamics. We will particularly focus on the case of surfaces as well as cases which incorporate the recent result of A. Levin for the powers of the multiplicative group.