منابع مشابه
Syzygies of Abelian Varieties
Let A be an ample line bundle on an abelian variety X (over an algebraically closed field). A theorem of Koizumi ([Ko], [S]), developing Mumford’s ideas and results ([M1]), states that if m ≥ 3 the line bundle L = A⊗m embeds X in projective space as a projectively normal variety. Moreover, a celebrated theorem of Mumford ([M2]), slightly refined by Kempf ([K4]), asserts that the homogeneous ide...
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In this paper we generalize parts of Mumford’s theory of the equations defining abelian varieties. Using the concept of a strongly symmetric line bundle, which is weaker than Mumford’s concept of totally symmetric line bundle and is introduced here for the first time, we extend Mumford’s methods of obtaining equations to arbitrary levels and to ample strongly symmetric line bundles. The first t...
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We prove: Let A be an abelian variety over a number field K. Then K has a finite Galois extension L such that for almost all σ ∈ Gal(L) there are infinitely many prime numbers l with Al(K̃(σ)) 6= 0. Here K̃ denotes the algebraic closure of K and K̃(σ) the fixed field in K̃ of σ. The expression “almost all σ” means “all but a set of σ of Haar measure 0”. MR Classification: 12E30 Directory: \Jarden\D...
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Throughout the paper we will freely use the following observation [21, p. 174]: if an abelian variety X is isogenous to a self-product Z of an abelian variety Z then a choice of an isogeny between X and Z defines an isomorphism between End(X) and the algebra Md(End (Z)) of d× d matrices over End(Z). Since the center of End(Z) coincides with the center of Md(End (Z)), we get an isomorphism betwe...
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ژورنال
عنوان ژورنال: Acta Arithmetica
سال: 2015
ISSN: 0065-1036,1730-6264
DOI: 10.4064/aa171-1-2