学术活动
数论与代数几何讨论班：Ramification and nearby cycles for l-adic sheaves on relative curves
2015-04-03
来源：科技处 供稿：冀俊宇 点击次数：主讲人：胡昊宇 博士（南开大学&法国巴黎十一大）
时 间：4月9日（周四）10:30-11:30
地 点：必赢76net线路官网北二区教学楼 513 教室
摘 要: I will present a new approach for a formula of Deligne and Kato that computes the dimension of the nearby cycle complex of an l-adic sheaf on a smooth relative curve over a strictly henselian trait such that $p$ is not one of its uniformizer. Deligne considered the case where the sheaf has no vertical ramification and Kato extended the formula to the general case. My approach is based on ramification theory of Abbes and Saito. It computes the nearby cycle complex in terms of the refined Swan conductor. In fact, I compare Abbes-Saito's refined Swan conductor with Kato's Swan conductor with differential values, which is the key ingredient in Kato's formula; the case of rank one sheaves is due to Abbes and Saito. My approach provides also a new independent proof of Deligne-Kato's formula.
