【报告摘要】 A complex algebraic variety X is hyperbolic (in the sense of Brody) if every holomorphic map from C to X is constant. Starting from the formal analogy between the S-unit equation theorem in the theory of Diophantine equations and the Picard-Borel theorem in complex analysis, it has been conjectured that among the algebraic varieties defined over number fields the hyperbolic ones should be those satisfying the following finiteness property: for every number field k the set of k-rational points is finite. We shall survey on some classical results in this direction and present some more recent ones.

【报告人简介】Pietro Corvaja is presently professor in Geometry at the University of Udine who also serves as the head of Department of Mathematics, Computer Science and Physics. He studied in Pisa and then in Paris, where he obtained in 1995 a PhD in mathematics under the guidance of Michel Laurent and Michel Waldschmidt, with a thesis on Diophantine approximation. He was post-doc in Venice with U. Zannier and then in Princeton with. E. Bombieri. He has a long lasting collaboration with U. Zannier, especially on Diophantine geometry. He is actively working on the arithmetic of algebraic groups, on elliptic schemes, on some aspects of complex and algebraic geometry. His work had been published in prestigious journals including Acta Math., Ann. Math., Invent. Math. etc.