首师大数论组讨论班（2015-04-09）

[SHUN TANG]

诸位好，本学期首都师范大学第四次数论与代数几何讨论班将于下周举行：
 
时间：2015年4月9日 周四 上午10：30--11：30
地点：首都师范大学北二区教学楼513教室（此校区在西三环紫竹桥南首师大北一区的街对面，走一个过街天桥即到）
 
报告人：胡昊宇 博士 (南开大学&法国巴黎十一大)
 
题目：Ramification and nearby cycles for l-adic sheaves on relative curves
 
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.

请将此信息转发给其他感兴趣的老师和学生，期待与大家相会！
 
祝好！
 
唐舜

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Shun TANG

School of Mathematical Sciences
Capital Normal University
No. 105, West 3rd Ring North Road
100048, Beijing
P. R. China