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Deuring's mass formula of a Mumford family


Authors: Mao Sheng and Kang Zuo
Journal: Trans. Amer. Math. Soc. 368 (2016), 169-207
MSC (2010): Primary 14G35; Secondary 14D07
DOI: https://doi.org/10.1090/S0002-9947-2015-06312-0
Published electronically: March 26, 2015
MathSciNet review: 3413860
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Abstract: We study the Newton polygon jumping locus of a Mumford family in char $ p$. Our main result says that, under a mild assumption on $ p$, the jumping locus consists of only supersingular points and its cardinality is equal to $ (p^r-1)(g-1)$, where $ r$ is the degree of the defining field of the base curve of a Mumford family in char $ p$ and $ g$ is the genus of the curve. The underlying technique is the $ p$-adic Hodge theory.


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Additional Information

Mao Sheng
Affiliation: School of Mathematical Sciences, University of Science and Technology of China, Hefei, 230026, People’s Republic of China
Email: msheng@ustc.edu.cn

Kang Zuo
Affiliation: Institut für Mathematik, Universität Mainz, Mainz, 55099, Germany
Email: zuok@uni-mainz.de

DOI: https://doi.org/10.1090/S0002-9947-2015-06312-0
Received by editor(s): September 26, 2013
Received by editor(s) in revised form: October 27, 2013
Published electronically: March 26, 2015
Additional Notes: The first-named author was supported by the National Natural Science Foundation of China (Grant No. 11471298). The second-named author was supported by the SFB/TR 45 ‘Periods, Moduli Spaces and Arithmetic of Algebraic Varieties’ of the DFG
Article copyright: © Copyright 2015 American Mathematical Society

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