Constructible sheaves on nilpotent cones in rather good characteristic

详细信息    查看全文

• 作者：Pramod N. Achar ; Anthony Henderson ; Daniel Juteau ; Simon Riche
• 关键词：Mathematics Subject ClassificationPrimary 17B08 ; 20G05
• 刊名：Selecta Mathematica
• 出版年：2017
• 出版时间：January 2017
• 年：2017
• 卷：23
• 期：1
• 页码：203-243
• 全文大小：
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics, general;
• 出版者：Springer International Publishing
• ISSN：1420-9020
• 卷排序：23

文摘

We study some aspects of modular generalized Springer theory for a complex reductive group G with coefficients in a field \(\Bbbk \) under the assumption that the characteristic \(\ell \) of \(\Bbbk \) is rather good for G, i.e. \(\ell \) is good and does not divide the order of the component group of the centre of G. We prove a comparison theorem relating the characteristic-\(\ell \) generalized Springer correspondence to the characteristic-0 version. We also consider Mautner’s characteristic-\(\ell \) ‘cleanness conjecture’; we prove it in some cases; and we deduce several consequences, including a classification of supercuspidal sheaves and an orthogonal decomposition of the equivariant derived category of the nilpotent cone.