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Irreducibility of Newton strata in $ {GU}(1,n-1)$ Shimura varieties


Author: Jeffrey D. Achter
Journal: Proc. Amer. Math. Soc. Ser. B 1 (2014), 79-88
MSC (2010): Primary 14K10; Secondary 14G17, 14L05, 11G10
DOI: https://doi.org/10.1090/S2330-1511-2014-00011-0
Published electronically: August 5, 2014
MathSciNet review: 3240772
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Abstract: Let $ L$ be a quadratic imaginary field, inert at the rational prime $ p$. Fix an integer $ n\ge 3$, and let $ \mathcal M$ be the moduli space (in characteristic $ p$) of principally polarized abelian varieties of dimension $ n$ equipped with an action by $ \mathcal {O}_L$ of signature $ (1,n-1)$. We show that each Newton stratum of $ \mathcal M$, other than the supersingular stratum, is irreducible.


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Additional Information

Jeffrey D. Achter
Affiliation: Department of Mathematics, Colorado State University, Fort Collins, Colorado 80523
Email: j.achter@colostate.edu

DOI: https://doi.org/10.1090/S2330-1511-2014-00011-0
Received by editor(s): November 7, 2013
Received by editor(s) in revised form: February 7, 2014
Published electronically: August 5, 2014
Additional Notes: This work was partially supported by a grant from the Simons Foundation (204164). The author also acknowledges support from the Colorado State University Libraries Open Access Research and Scholarship Fund.
Communicated by: Lev Borisov
Article copyright: © Copyright 2014 by the author under Creative Commons Attribution-Noncommercial 3.0 License (CC BY NC 3.0)

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