题目：Representability and algebraic cycles

报告人：杨森（滁州学院）

时间：4月26日（周五）10:00-11:00

地点：科大东区5205

摘要：For X a smooth projective surface, Bloch investigated representability of the Chow group 〖CH〗^2 (X) by computing its formal completion functor (CH) ̂^2. This motivated him to make the well-known conjecture which predicted that, for X (over complex number field) with trivial geometric genus, the Albanese map is an isomorphism. This conjecture had been intensively studied by experts, including Bloch, Kas, Lieberman, Wenchuan Hu (胡文传), Pedrini, Weibel, Voisin.Green and Griffiths pioneered to study the first order deformations of zero cycles on a surface and pointed out that it was a nonclassical phenomena. We connect their idea with the work of Bloch by studying representability of algebraic cycles. The main tools used here are the classical Bloch-Ogus theorem and Schlessinger’s theory on functors of Artin rings.