Abstract
We endow the set of lattices in $\mathbb{Q}_p^n$ 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.
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@ARTICLE{Ap, mrkey = {3272912},
number = {4},
issn = {2214-2584},
author = {Alper, Jarod},
mrclass = {14D20 (14A20 14L15 14L24 14L30)},
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author = {Beilinson, A. and Drinfeld, V.},
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} -
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} -
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@ARTICLE{CKV, mrkey = {3406443},
number = {9},
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author = {Chen, Miaofen and Kisin, Mark and Viehmann, Eva},
mrclass = {14G35 (20G25)},
doi = {10.1112/S0010437X15007253},
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@ARTICLE{CLO, mrkey = {2979821},
number = {4},
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year = {2012},
pages = {747--814},
} -
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@INCOLLECTION{Ka, mrkey = {0563463},
author = {Katz, Nicholas M.},
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series = {Astérisque},
address = {Paris},
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author = {Kazhdan, David and Lusztig, George},
mrclass = {14M15 (55N35 57R19)},
series = {Proc. Sympos. Pure Math.},
address = {Providence, RI},
publisher = {Amer. Math. Soc.},
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volume = {XXXVI},
mrnumber = {0573434},
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venue = {{P}roc. {S}ympos. {P}ure {M}ath., {U}niv. {H}awaii, {H}onolulu, {H}awaii, 1979},
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} -
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author = {Lusztig, George},
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series = {Astérisque},
address = {Paris},
publisher = {Soc. Math. France},
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{III}},
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venue = {{L}uminy, 1981},
title = {Singularities, character formulas, and a {$q$}-analog of weight multiplicities},
pages = {208--229},
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number = {3},
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title = {A bar operator for involutions in a {C}oxeter group},
year = {2012},
pages = {355--404},
} -
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journal = {Bull. Inst. Math. Acad. Sin.},
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year = {2012},
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URL ={http://web.math.sinica.edu.tw/bulletin/archives_articlecontent16.jsp?bid=MjAxMjMwMQ==},
} -
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year = {2013},
pages = {311--340},
} -
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