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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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Deuring’s mass formula of a Mumford family
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by Mao Sheng and Kang Zuo PDF
Trans. Amer. Math. Soc. 368 (2016), 169-207 Request permission

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
  • MR Author ID: 269893
  • Email: zuok@uni-mainz.de
  • 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
  • © Copyright 2015 American Mathematical Society
  • 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
  • MathSciNet review: 3413860