中央研究院數學研究所

Special Colloquium

Rational points on surfaces

2026/02/26 (Thu.) 15:30~16:30

Date : 2026/02/26 (Thu.) 15:30~16:30
Location : Seminar Room 638, Institute of Mathematics (NTU Campus)
Speaker : Alexei N. Skorobogatov (Imperial College London)
Abstract : Rational points are solutions of Diophantine equations in rational numbers and other fields of interest for number theory. The talk will survey the local-to-global principle for rational points, also known as the Hasse principle, with focus on surfaces. The story starts with Legendre who gave a necessary and sufficient condition for solubility of conics in integers, an early precursor of the Hasse-Minkowski theorem. After describing the state of the art for conic bundle surfaces (families of conics over a curve), emphasising the role played by the Brauer group and the Brauer-Manin obstruction, I will talk about more recent results that go beyond conic bundles and are related to abelian varieties and Kummer surfaces.