学术报告
The Nori fundamental gerbe-张磊博士（德国柏林自由大学）
题目：The Nori fundamental gerbe
报告人：张磊博士（德国柏林自由大学）
摘要：In the paper "The Nori fundamental gerbe of a fibered category" N. Borne and A. Vistoli generalized the notion of Nori fundamental group on schemes to that of Nori fundamental gerbe on fibered categories, and they gave a Tannakian interpretation of the fundamental gerbe when the fibered category is pseudo-poper. Here a fibered category X is called "pseudo-poper" if it is quasi-compact and if the space of global sections of any vector bundle on X is a finite dimensional vector space. This is not a significant generalization if the fibered category is a scheme, but it is so when we consider stacks. In fact this notion includes a large class of extremely important stacks, namely the affine gerbes. In the leture we will first introduce the techniques developped by Borne-Vistoli, then we will introduce a generalization of the Tannakian interpretation to non pseudo-proper fibered categories which is due to Fabio Tonini and me. In the end we will also introduce a Lange und Stuhler style theorem for algebraic stacks which roughly says that a vector bundle comes from the representation of the fundamental group if and only if it is trivialized by a finite surjective cover. We managed to do this for even non pseudo-proper algebraic stacks.
时间：3月30日（周四）下午4:30-5:30
地点：首都师范大学本部新教二楼610教室
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