Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

Dimensions of automorphism group schemes of finite level truncations of $ F$-cyclic $ F$-crystals


Authors: Zeyu Ding and Xiao Xiao
Journal: Trans. Amer. Math. Soc. 374 (2021), 269-302
MSC (2010): Primary 14L15
DOI: https://doi.org/10.1090/tran/8243
Published electronically: October 26, 2020
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: Let $ \mathcal {M}_{\pi }$ be an $ F$-cyclic $ F$-crystal over an algebraically closed field of positive characteristic defined by a permutation $ \pi $ and a set of prescribed Hodge slopes. We prove combinatorial formulas for the dimension $ \gamma _{\mathcal {M}_{\pi }}(m)$ of the automorphism group scheme of $ \mathcal {M}_{\pi }$ at finite level $ m$ and the number of connected components of the endomorphism group scheme at finite level $ m$. As an application, we show that if $ \mathcal {M}_{\pi }$ is a nonordinary Dieudonné module defined by a cycle $ \pi $, then $ \gamma _{\mathcal {M}_{\pi }}(m+1) - \gamma _{\mathcal {M}_{\pi }}(m) < \gamma _{\mathcal {M}_{\pi }}(m) - \gamma _{\mathcal {M}_{\pi }}(m-1)$ for all $ 1 \leq m \leq n_{\mathcal {M}_{\pi }}$, where $ n_{\mathcal {M}_{\pi }}$ is the isomorphism number of $ \mathcal {M}_{\pi }$.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC (2010): 14L15

Retrieve articles in all journals with MSC (2010): 14L15


Additional Information

Zeyu Ding
Affiliation: Department of Computer Science and Engineering, Pennsylvania State University, University Park, Pennsylvania 16802
Email: zyding@psu.edu

Xiao Xiao
Affiliation: Department of Mathematics, Utica College, 1600 Burrstone Road, Utica, New York 13502
Email: xixiao@utica.edu

DOI: https://doi.org/10.1090/tran/8243
Received by editor(s): July 22, 2019
Received by editor(s) in revised form: December 1, 2019, and March 16, 2020
Published electronically: October 26, 2020
Article copyright: © Copyright 2020 American Mathematical Society