GV-subschemes and their embeddings in principally polarized abelian varieties

Residual representations of semistable principally polarized abelian varieties

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Principally Polarized Ordinary Abelian Varieties over Finite Fields

Deligne has shown that there is an equivalence from the category of ordinary abelian varieties over a finite field A: to a category of Z-modules with additional structure. We translate several geometric notions, including that of a polarization, into Deligne's category of Z-modules. We use Deligne's equivalence to characterize the finite group schemes over k that occur as kernels of polarizatio...

Polarizations on abelian subvarieties of principally polarized abelian varieties with dihedral group actions

For any n ≥ 2 we study the group algebra decomposition of an ([ 2 ] + 1)dimensional family of principally polarized abelian varieties of dimension n with an action of the dihedral group of order 2n. For any odd prime p, n = p and n = 2p we compute the induced polarization on the isotypical components of these varieties and some other distinguished subvarieties. In the case of n = p the family c...

On Isogenous Principally Polarized Abelian Surfaces

We study a relationship between two genus 2 curves whose jacobians are isogenous with kernel equal to a maximal isotropic subspace of p-torsion points with respect to the Weil pairing. For p = 3 we find an explicit relationship between the set of Weierstrass points of the two curves extending the classical results of F. Richelot (1837) and G. Humbert (1901) in the case p = 2.

Local positivity of principally polarized abelian threefolds