Displaying similar documents to “On reduction of Hilbert-Blumenthal varieties”

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...

Endomorphism algebras of motives attached to elliptic modular forms

Alexander F. Brown, Eknath P. Ghate (2003)

Annales de l’institut Fourier

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We study the endomorphism algebra of the motive attached to a non-CM elliptic modular cusp form. We prove that this algebra has a sub-algebra isomorphic to a certain crossed product algebra X . The Tate conjecture predicts that X is the full endomorphism algebra of the motive. We also investigate the Brauer class of X . For example we show that if the nebentypus is real and p is a prime that does not divide the level, then the local behaviour of X at a place lying above p is essentially...

On the osculatory behaviour of higher dimensional projective varieties.

Edoardo Ballico, Claudio Fontanari (2004)

Collectanea Mathematica

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We explore the geometry of the osculating spaces to projective verieties of arbitrary dimension. In particular, we classify varieties having very degenerate higher order osculating spaces and we determine mild conditions for the existence of inflectionary points.

The lifted root number conjecture for fields of prime degree over the rationals: an approach via trees and Euler systems

Cornelius Greither, Radiu Kučera (2002)

Annales de l’institut Fourier

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The so-called Lifted Root Number Conjecture is a strengthening of Chinburg’s Ω ( 3 ) - conjecture for Galois extensions K / F of number fields. It is certainly more difficult than the Ω ( 3 ) -localization. Following the lead of Ritter and Weiss, we prove the Lifted Root Number Conjecture for the case that F = ℚ and the degree of K / F is an odd prime, with another small restriction on ramification. The very explicit calculations with cyclotomic units use trees and some classical combinatorics for bookkeeping....