Algebraic cycles and Hodge structures III
主 题: Algebraic cycles and Hodge structures III
报告人: Claire Voisin (CNRS)
时 间: 2013-10-15 09:30-11:30
地 点: Quan 9, BICMR（数学中心活动）
The Chow groups of a smooth projective variety are very refined invariants whose counterpart in complex geometry is the data of the Hodge structures on cohomology. In fact, there are rather precise conjectures linking both kinds of objects. We will describe these conjectures and explain some technics to attack them in particular cases.
III. The Bloch-Beilinson conjectures
This is a fundamental set of conjectures stating conversely that if the cohomology has large coniveau (small niveau) then the Chow groups are small. I will explain many formulations, in particular the nilpotence conjecture, and what can be said on \"Bloch-Beilinson\'s filtrations\".