Cycle classes of the E-O stratification on the moduli of abelian varieties. (English) Zbl 1200.14089

Ekedahl, Torsten; van der Geer, Gerard

Tschinkel, Yuri (ed.) et al., Algebra, arithmetic, and geometry. In honor of Yu. I. Manin on the occasion of his 70th birthday. Vol. I. Boston, MA: Birkhäuser (ISBN 978-0-8176-4744-5/hbk; 978-0-8176-4745-2/ebook). Progress in Mathematics 269, 567-636 (2009).

The authors introduce a stratification on the space of symplectic flags on the de Rham bundle of the universal principally polarized abelian variety in positive characteristic. They study some geometric properties of this stratification, such as irreducibility of the strata, and they calculate the cycle classes. Then they relate this stratification with the E-O stratification on the moduli space of principally polarized abelian varieties of a fixed dimension and derive properties of the latter.
For the entire collection see [Zbl 1185.00041].

Reviewer: Cristiana Bertolin (Padova)

MSC:

14K10	Algebraic moduli of abelian varieties, classification
14G35	Modular and Shimura varieties

Keywords:

moduli space of abelian varieties; E-O-stratification; cycle classes; Weyl group