Deuring's mass formula of a Mumford family
Mao Sheng, Kang Zuo

TL;DR
This paper investigates the Newton polygon jumping locus of a Mumford family in characteristic p, showing it consists solely of supersingular points with a specific cardinality, using p-adic Hodge theory.
Contribution
It establishes a precise description and count of the supersingular points in the Newton polygon jumping locus for Mumford families in characteristic p.
Findings
Jumping locus contains only supersingular points.
Cardinality of the jumping locus is (p^r - 1)(g - 1).
Technique used is p-adic Hodge theory.
Abstract
We study the Newton polygon jumping locus of a Mumford family in char . Our main result says that, under a mild assumption on , the jumping locus consists of only supersingular points and its cardinality is equal to , where is the degree of the defining field of the base curve of a Mumford family in char and is the genus of the curve. The underlying technique is the -adic Hodge theory.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Advanced Algebra and Geometry
