Abelian varieties of Weil type and Kuga-Satake varieties
نویسندگان
چکیده
منابع مشابه
Abelian Varieties of Weil Type and Kuga-satake Varieties
We analyze the relationship between abelian fourfolds of Weil type and Hodge structures of type K3, and we extend some of these correspondences to the case of arbitrary dimension.
متن کاملKuga-satake Varieties and the Hodge Conjecture
Kuga-Satake varieties are abelian varieties associated to certain weight two Hodge structures, for example the second cohomology group of a K3 surface. We start with an introduction to Hodge structures and we give a detailed account of the construction of Kuga-Satake varieties. The Hodge conjecture is discussed in section 2. An excellent survey of the Hodge conjecture for abelian varieties is [...
متن کاملReal multiplication on K3 surfaces and Kuga Satake varieties
The endomorphism algebra of a K3 type Hodge structure is a totally real field or a CM field. In this paper we give a low brow introduction to the case of a totally real field. We give existence results for the Hodge structures, for their polarizations and for certain K3 surfaces. We consider the Kuga Satake variety of these Hodge structures and we discuss some examples. Finally we indicate vari...
متن کاملTorsion of Abelian Varieties, Weil Classes and Cyclotomic Extensions
Let K ⊂ C be a field finitely generated over Q, K(a) ⊂ C the algebraic closure of K, G(K) = Gal(K(a)/K its Galois group. For each positive integer m we write K(μm) for the subfield of K(a) obtained by adjoining to K all mth roots of unity. For each prime l we write K(l) for the subfield of K(a) obtained by adjoining to K all l−power roots of unity. We write K(c) for the subfield of K(a) obtaine...
متن کاملOn the Structure of Weil Restrictions of Abelian Varieties
We give a description of endomorphism rings of Weil restrictions of abelian varieties with respect to finite Galois extensions of fields. The results are applied to study the isogeny decompositions of Weil restrictions. 2000 Mathematics Subject Classification Primary: 14K15, Secondary: 11G10.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Tohoku Mathematical Journal
سال: 2001
ISSN: 0040-8735
DOI: 10.2748/tmj/1178207420