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Affine Grassmannians and the geometric Satake in mixed characteristic

Zhu, Xinwen (2017) Affine Grassmannians and the geometric Satake in mixed characteristic. Annals of Mathematics, 185 (2). pp. 403-492. ISSN 0003-486X. https://resolver.caltech.edu/CaltechAUTHORS:20140919-164523625

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Abstract

We endow the set of lattices in Q^n_p with a reasonable algebro-geometric structure. As a result, we prove the representability of affine Grassmannians and establish the geometric Satake equivalence in mixed characteristic. We also give an application of our theory to the study of Rapoport-Zink spaces.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.4007/annals.2017.185.2.2DOIArticle
http://annals.math.princeton.edu/2017/185-2/p02PublisherArticle
http://arxiv.org/abs/1407.8519arXivDiscussion Paper
Additional Information:© 2017 Department of Mathematics, Princeton University. Received: 24 October 2014; Revised: 24 June 2016; Accepted: 5 July 2016; Published online: 7 February 2017. An ongoing project with L. Xiao is the main motivation of the current paper. The author thanks him cordially for the collaboration. The author also thanks B. Bhatt, B. Conrad, V. Drinfeld, B. Elias, A. de Jong, X. He, J. Kamnitzer, L. Moret-Bailly, G. Pappas, P. Scholze and Z. Yun for useful discussions and comments. He in particular would like to thank J. Kamnitzer for pointing out a serious mistake in an early draft of the paper. The author is partially supported by NSF grant DMS-1001280/1313894 and DMS-1303296/1535464 and the AMS Centennial Fellowship.
Funders:
Funding AgencyGrant Number
NSFDMS-1001280
NSFDMS-1313894
NSFDMS-1303296
NSFDMS-1535464
AMS Centennial FellowshipUNSPECIFIED
Subject Keywords:affine Deligne-Lusztig variety, affine Grassmannian, geometric Satake correspondence, perfect algebraic geometry
Issue or Number:2
Record Number:CaltechAUTHORS:20140919-164523625
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20140919-164523625
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:49883
Collection:CaltechAUTHORS
Deposited By: George Porter
Deposited On:20 Sep 2014 01:58
Last Modified:03 Oct 2019 07:18

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