On the p-supports of a holonomic D-module
成果类型：
Article
署名作者：
Bitoun, Thomas
署名单位：
University of Oxford
刊物名称：
INVENTIONES MATHEMATICAE
ISSN/ISSBN：
0020-9910
DOI：
10.1007/s00222-018-0837-6
发表日期：
2019
页码：
779-818
关键词：
摘要：
For a smooth variety Y over a perfect field of positive characteristic, the sheaf DY of crystalline differential operators on Y (also called the sheaf of PD-differential operators) is known to be an Azumaya algebra over TY, the cotangent space of the Frobenius twist Y of Y. Thus to a sheaf of modules M over DY one can assign a closed subvariety of TY, called the p-support, namely the support of M seen as a sheaf on TY. We study here the family of p-supports assigned to the reductions modulo primes p of a holonomic D-module. We prove that the Azumaya algebra of differential operators splits on the regular locus of the p-support and that the p-support is a Lagrangian subvariety of the cotangent space, for p large enough. The latter was conjectured by Kontsevich. Our approach also provides a new proof of the involutivity of the singular support of a holonomic D-module, by reduction modulo p.