Week 3: Moduli Interpretation of Shimura Varieties
نویسنده
چکیده
Moduli interpretation. Lecture 7 (Sep. 29, 2008) – continued
منابع مشابه
Shimura Varieties and Moduli
Connected Shimura varieties are the quotients of hermitian symmetric domains by discrete groups defined by congruence conditions. We examine their relation with moduli varieties.
متن کاملFinal Version; Final Form. Shimura Varieties and Motives
Deligne has expressed the hope that a Shimura variety whose weight is defined over Q is the moduli variety for a family of motives. Here we prove that this is the case for “most” Shimura varieties. As a consequence, for these Shimura varieties, we obtain an explicit interpretation of the canonical model and a modular description of its points in any field containing the reflex field. Moreover, ...
متن کاملOn Finiteness Conjectures for Modular Quaternion Algebras
It is conjectured that there exist finitely many isomorphism classes of simple endomorphism algebras of abelian varieties of GL2-type over Q of bounded dimension. We explore this conjecture when particularized to quaternion endomorphism algebras of abelian surfaces by giving a moduli interpretation which translates the question into the diophantine arithmetic of Shimura curves embedded in Hilbe...
متن کاملOn Finiteness Conjectures for Endomorphism Algebras of Abelian Surfaces
It is conjectured that there exist only finitely many isomorphism classes of endomorphism algebras of abelian varieties of bounded dimension over a number field of bounded degree. We explore this conjecture when restricted to quaternion endomorphism algebras of abelian surfaces of GL2type over Q by giving a moduli interpretation which translates the question into the diophantine arithmetic of S...
متن کاملModuli Fields of Cm-motives Applied to Hilbert's 12-th Problem
We apply the theorem of Shimura and Taniyama to compute the largest abelian extension of a CM-eld E which can be obtained by evaluating E-rational automorphic functions at certain special points of Shimura varieties. Abelian class eld theory classiies the abelian extensions of a number eld k, but does not explain how to generate the elds. In his Jugendtraum, Kronecker suggested that the abelian...
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تاریخ انتشار 2008