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EXTREMAL CASES OF RAPOPORT–ZINK SPACES

Part of: Arithmetic problems. Diophantine geometry Arithmetic algebraic geometry Linear algebraic groups and related topics

Published online by Cambridge University Press:  20 January 2021

Ulrich Görtz Open the ORCID record for Ulrich Görtz [Opens in a new window] ,
Xuhua He  and
Michael Rapoport
Ulrich Görtz
Affiliation:
Institut für Experimentelle Mathematik, Universität Duisburg-Essen, 45117Essen, Germany (ulrich.goertz@uni-due.de)
Xuhua He
Affiliation:
The Institute of Mathematical Sciences and Department of Mathematics, The Chinese University of Hong Kong, Shatin, N.T., Hong Kong (xuhuahe@math.cuhk.edu.hk)
Michael Rapoport
Affiliation:
Mathematisches Institut der Universität Bonn, Endenicher Allee 60, 53115Bonn, Germany and Department of Mathematics, University of Maryland, College Park, MD20742, USA (rapoport@math.uni-bonn.de)
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Abstract

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We investigate qualitative properties of the underlying scheme of Rapoport–Zink formal moduli spaces of p-divisible groups (resp., shtukas). We single out those cases where the dimension of this underlying scheme is zero (resp., those where the dimension is the maximal possible). The model case for the first alternative is the Lubin–Tate moduli space, and the model case for the second alternative is the Drinfeld moduli space. We exhibit a complete list in both cases.

Keywords

Rapoport-Zink spacesDrinfeld spaceLubin-Tate spaceaffine Deligne-Lusztig varietiesaffine Weyl group

MSC classification

Primary: 14G35: Modular and Shimura varieties
Secondary: 20G25: Linear algebraic groups over local fields and their integers 11G18: Arithmetic aspects of modular and Shimura varieties
Type
Research Article
Information
Journal of the Institute of Mathematics of Jussieu , Volume 21 , Issue 5 , September 2022 , pp. 1727 - 1782
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Creative Commons
Creative Common License - CCCreative Common License - BYCreative Common License - NCCreative Common License - ND
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Copyright
© The Author(s), 2021. Published by Cambridge University Press

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