In 2002, in the paper entitled ＂A subspace theorem approach to integral points on curves＂, Corvaja and Zannier started the program of studying integral points on algebraic varieties by using Schmidt＇s subspace theo...In 2002, in the paper entitled ＂A subspace theorem approach to integral points on curves＂, Corvaja and Zannier started the program of studying integral points on algebraic varieties by using Schmidt＇s subspace theorem in Diophantine approximation. Since then, the program has led a great progress in the study of Diophantine approximation. It is known that the counterpart of Schmidt＇s subspace in Nevanlinna theory is H. Cartan＇s Second Main Theorem. In recent years, the method of Corvaja and Zannier has been adapted by a number of authors and a big progress has been made in extending the Second Main Theorem to holomorphic mappings from C into arbitrary projective variety intersecting general divisors by using H. Cartan＇s original theorem. We call such method ＂a Cartan＇s Second Main Theorem approach＂. In this survey paper, we give a systematic study of such approach, as well as survey some recent important results in this direction including the recent work of the author with Paul Voja.展开更多
基金supported in part by the Simons Foundation Mathematics and Physical Sciences-Collaboration Grants for Mathematicians
文摘In 2002, in the paper entitled ＂A subspace theorem approach to integral points on curves＂, Corvaja and Zannier started the program of studying integral points on algebraic varieties by using Schmidt＇s subspace theorem in Diophantine approximation. Since then, the program has led a great progress in the study of Diophantine approximation. It is known that the counterpart of Schmidt＇s subspace in Nevanlinna theory is H. Cartan＇s Second Main Theorem. In recent years, the method of Corvaja and Zannier has been adapted by a number of authors and a big progress has been made in extending the Second Main Theorem to holomorphic mappings from C into arbitrary projective variety intersecting general divisors by using H. Cartan＇s original theorem. We call such method ＂a Cartan＇s Second Main Theorem approach＂. In this survey paper, we give a systematic study of such approach, as well as survey some recent important results in this direction including the recent work of the author with Paul Voja.
