Irreducibility of Newton strata in $\textrm {GU}(1,n-1)$ Shimura varieties
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- by Jeffrey D. Achter HTML | PDF
- Proc. Amer. Math. Soc. Ser. B 1 (2014), 79-88
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.References
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Additional Information
- Jeffrey D. Achter
- Affiliation: Department of Mathematics, Colorado State University, Fort Collins, Colorado 80523
- MR Author ID: 690384
- Email: j.achter@colostate.edu
- 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
- © Copyright 2014 by the author under Creative Commons Attribution-Noncommercial 3.0 License (CC BY NC 3.0)
- 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
- MathSciNet review: 3240772