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Deuring’s mass formula of a mumford family

Mao Sheng University of Science and Technology of China Kang Zuo University of Mainz

mathscidoc:1811.01002

Distinguished Paper Award in 2018

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 368, (1), 169–207, 2016.1
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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@inproceedings{mao2016deuring’s,
  title={DEURING’S MASS FORMULA OF A MUMFORD FAMILY},
  author={Mao Sheng, and Kang Zuo},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20181102173143832954173},
  booktitle={TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY},
  volume={368},
  number={1},
  pages={169–207},
  year={2016},
}
Mao Sheng, and Kang Zuo. DEURING’S MASS FORMULA OF A MUMFORD FAMILY. 2016. Vol. 368. In TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY. pp.169–207. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20181102173143832954173.
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