Deuring's mass formula of a Mumford family

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.

arXiv comment36 pages. This is the final version of our early manuscript with title "On the Newton stratification of a Shimura curve of Hodge type: the case of corestriction". We thank warmly the anonymous referees for their great efforts to improve the quality of the work. It is accepted for publication by Transactions of the AMS