Speculations on the mod $p$ representation theory of $p$-adic groups
Speculations on the mod $p$ representation theory of $p$-adic groups
复制标题
对$p$-adic群的mod $p$表示论的推测
DOI：
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发表时间：
2016
期刊：
影响因子：
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通讯作者：
M. Harris
中科院分区：
文献类型：
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作者：
M. Harris
- 从假设开始，最近的工作的启发几何朗兰兹对应，模拟模p表示的p-adic群的本地朗兰兹对应可能是一个等价的（更高）类别，而不是双射集，本文提出了一系列的猜测和问题的性质，这样一个假设的等价。对应的伽罗瓦侧将是埃默顿和吉构造的ind-代数栈上的层的范畴，或者可能是其派生变体;对应的自守侧将是施耐德研究的派生赫克代数上的dg-模的派生范畴。双方都相当神秘，但本文提出的一些问题可能是可以理解的。(1)导致这些结果的研究已获得欧洲研究理事会在欧洲共同体第七框架计划（FP 7/2007-2013）/ ERC赠款协议n 290766（AAMOT）下的资助。作者得到了NSF资助DMS-1404769的部分支持
— Starting with the hypothesis, inspired by recent work on the geometric Langlands correspondence, that the analogue for mod p representations of p-adic groups of the local Langlands correspondence might be an equivalence of (higher) categories rather than a bijection of sets, this paper presents a series of speculations and questions about the properties of such a hypothetical equivalence. The Galois side of the correspondence would be a category of sheaves on the ind-algebraic stack constructed by Emerton and Gee, or perhaps a derived variant thereof; the automorphic side of the correspondence would be a derived category of dg-modules over the derived Hecke algebra studied by Schneider. Both sides are quite mysterious, but some of the questions proposed in this paper may be accessible. (1) The research leading to these results has received funding from the European Research Council under the European Community’s Seventh Framework Programme (FP7/2007-2013) / ERC Grant agreement n 290766 (AAMOT). The author was partially supported by NSF grant DMS-1404769
栈态射的“图式理论图像”
影响因子：
1.5
作者：
Emerton, Matthew;Gee, Toby
通讯作者：
Gee, Toby