Deuring’s mass formula of a Mumford family

Abstract

We study the Newton polygon jumping locus of a Mumford family in char p p . Our main result says that, under a mild assumption on p p , the jumping locus consists of only supersingular points and its cardinality is equal to ( p r − 1 ) ( g − 1 ) (p^r-1)(g-1) , where r r is the degree of the defining field of the base curve of a Mumford family in char p p and g g is the genus of the curve. The underlying technique is the p p -adic Hodge theory.