Displaying similar documents to “Some remarks on the moduli space of principally polarized abelian varieties with level ( 2 , 4 ) -structure”

The small Schottky-Jung locus in positive characteristics different from two

Fabrizio Andreatta (2003)

Annales de l’institut Fourier

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We prove that the locus of Jacobians is an irreducible component of the small Schottky locus in any characteristic different from 2 . The proof follows an idea of B. van Geemen in characteristic 0 and relies on a detailed analysis at the boundary of the q - expansion of the Schottky-Jung relations. We obtain algebraically such relations using Mumford’s theory of 2 -adic theta functions. We show how the uniformization theory of semiabelian schemes, as developed by D. Mumford, C.-L. Chai...

On reduction of Hilbert-Blumenthal varieties

Chia-Fu Yu (2003)

Annales de l'Institut Fourier

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Let O 𝐅 be the ring of integers of a totally real field 𝐅 of degree g . We study the reduction of the moduli space of separably polarized abelian O 𝐅 -varieties of dimension g modulo p for a fixed prime p . The invariants and related conditions for the objects in the moduli space are discussed. We construct a scheme-theoretic stratification by a -types on the Rapoport locus and study the relation with the slope stratification. In particular, we recover the main results of Goren and Oort [J....

Relations between jacobians of modular curves of level p 2

Imin Chen, Bart De Smit, Martin Grabitz (2004)

Journal de Théorie des Nombres de Bordeaux

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We derive a relation between induced representations on the group GL 2 ( ℤ / p 2 ℤ ) which implies a relation between the jacobians of certain modular curves of level p 2 . The motivation for the construction of this relation is the determination of the applicability of Mazur’s method to the modular curve associated to the normalizer of a non-split Cartan subgroup of GL 2 ( ℤ / p 2 ℤ ) .