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短课程:Constructing crystalline representations of the etale fundamental group of a p-adic curve via stable Higgs bundles

左康教授(Mainz大学数学系)
Tuesday, March 21st, 2017, 1:00 PM  闵行校区数学楼401室
 
数学系与“核心数学与实践”重点实验室短课程

课程名称:Constructing crystalline representations of the etale fundamental group of a p-adic curve via stable Higgs bundles.

时间: 3月21日(周二)下午 13:00—15:00
3月22日(周三)上午 09:00—11:00
3月28日(周二)下午 13:00—15:00
3月29日(周三)上午 09:00—11:00

摘 要

In a joint program with G-T. Lan and M. Sheng we have established a p-adic Hitchin- Simpson correspondence : given a smooth proper scheme X over the Witt ring W of a finite field F_q of characteristic p, then the category of GL_r-crystalline representations of the etale fundamental group of X over the fraction field K of W is equivalent to the category of periodic graded Higgs bundles on X. In a recent joint paper with R-R.Sun and J-B.Yang we have worked out a PGL-version of the p-adic Hitchin- Simpson correspondence between the category of PGL_r-crystalline representations of the etale fundamental group of X/K and the category of periodic graded Higgs bundles after twisting line bundles. As an application one shows that the etale fundamental group of any smooth p-adic curve C of genus >1 carries irreducible PGL_r-crystalline representations for some 1<r .

华东师范大学数学系
上海市核心数学与实践重点实验室
   
 
 
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