Moduli of Supersingular Abelian Varieties

by Ke-Zheng Li, Frans Oort

Overview

Abelian varieties can be classified via their moduli. In positive characteristic the structure of the p-torsion-structure is an additional, useful tool. For that structure supersingular abelian varieties can be considered the most special ones. They provide a starting point for the fine description of various structures. For low dimensions the moduli of supersingular abelian varieties is by now well understood. In this book we provide a description of the supersingular locus in all dimensions, in particular we compute the dimension of it: it turns out to be equal to Äg.g/4Ü, and we express the number of components as a class number, thus completing a long historical line where special cases were studied and general results were conjectured (Deuring, Hasse, Igusa, Oda-Oort, Katsura-Oort).

Product Details

ISBN-13:	9783540639237
Publisher:	Springer Berlin Heidelberg
Publication date:	03/05/1998
Series:	Lecture Notes in Mathematics , #1680
Edition description:	1998
Pages:	116
Product dimensions:	6.14(w) x 9.21(h) x 0.36(d)

Table of Contents

Supersingular abelian varieties.- Some prerequisites about group schemes.- Flag type quotients.- Main results on S g,1.- Prerequisites about Dieudonné modules.- PFTQs of Dieudonné modules over W.- Moduli of rigid PFTQs of Dieudonné modules.- Some class numbers.- Examples on S g,1.- Main results on S g,d.- Proofs of the propositions on FTQs.- Examples on S g,d (d>1).- A scheme-theoretic definition of supersingularity.