Journal of Algebraic Geometry

Journal of Algebraic Geometry

Online ISSN 1534-7486; Print ISSN 1056-3911

   
 

 

Deformation subspaces of $ p$-divisible groups as formal Lie groups associated to $ p$-divisible groups


Author: Adrian Vasiu
Journal: J. Algebraic Geom. 20 (2011), 1-45
DOI: https://doi.org/10.1090/S1056-3911-2010-00571-1
Published electronically: September 9, 2010
MathSciNet review: 2729274
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Abstract | References | Additional Information

Abstract: Let $ k$ be an algebraically closed field of characteristic $ p>0$. Let $ D$ be a $ p$-divisible group over $ k$ which is not isoclinic. Let $ \mathcal{D}$ (resp. $ \mathcal{D}_{k}$) be the formal deformation space of $ D$ over Spf$ (W(k))$ (resp. over Spf$ (k)$). We use axioms to construct formal subschemes $ \mathcal{G}_{k}$ of $ \mathcal{D}_{k}$ that: (i) have canonical structures of formal Lie groups over Spf$ (k)$ associated to $ p$-divisible groups over $ k$, and (ii) give birth, via all geometric points Spf$ (K)\to \mathcal{G}_{k}$, to $ p$-divisible groups over $ K$ that are isomorphic to $ D_{K}$. We also identify when there exist formal subschemes $ \mathcal{G}$ of $ \mathcal{D}$ which lift $ \mathcal{G}_{k}$ and which have natural structures of formal Lie groups over Spf$ (W(k))$ associated to $ p$-divisible groups over $ W(k)$. Applications to Traverso (ultimate) stratifications are included as well.


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Additional Information

Adrian Vasiu
Affiliation: Department of Mathematical Sciences, Binghamton University, P.O. Box 6000, Binghamton, New York 13902-6000
Email: adrian@math.binghamton.edu

DOI: https://doi.org/10.1090/S1056-3911-2010-00571-1
Received by editor(s): April 23, 2008
Received by editor(s) in revised form: November 12, 2009
Published electronically: September 9, 2010
Additional Notes: This project was partially supported by the NSF grant DMS #0900967.

Journal of Algebraic Geometry
The Journal of Algebraic Geometry
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