1.

Record Nr.

UNINA9910146297703321

Autore

Li Ke-Zheng <1949->

Titolo

Moduli of Supersingular Abelian Varieties / / by Ke-Zheng Li, Frans Oort

Pubbl/distr/stampa

Berlin, Heidelberg : , : Springer Berlin Heidelberg : , : Imprint : Springer, , 1998

ISBN

3-540-69666-0

Edizione

[1st ed. 1998.]

Descrizione fisica

1 online resource (IX, 116 p.)

Collana

Lecture Notes in Mathematics, , 1617-9692 ; ; 1680

Disciplina

516.35

Soggetti

Geometry, Algebraic

Algebraic Geometry

Lingua di pubblicazione

Inglese

Formato

Materiale a stampa

Livello bibliografico

Monografia

Note generali

Bibliographic Level Mode of Issuance: Monograph

Nota di contenuto

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.

Sommario/riassunto

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).