Some Cases of the Mumford-Tate Conjecture and Shimura Varieties
By A. Vasiu. 2002
48 citations recorded by the source corpus.
We prove the Mumford-Tate conjecture for those abelian varieties over number fields whose extensions to C have attached adjoint Shimura varieties that are products of simple, adjoint Shimura varieties of certain Shimura types. In particular, we prove the conjecture for the orthogonal case (i.e., for the Bn and D R Shimura types). As a main tool, we construct embeddings of Shimura varieties (whose adjoints are) of prescribed abelian type into unitary Shimura varieties of PEL type. These constructions implicitly classify the adjoints of Shimura varieties of PEL type.
Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/9433d3b4d60bed88d94bb0307ac459e9f1ce11b1
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In Discrete Mathematics and Combinatorics
In Geometry and Topology
In Mathematical Physics
Citations in the corpus
- On the Picard number of K3 surfaces over number fields (2011, background): “A lot of work has been done in its direction in the case of abelian varieties, see for instance [20], [18], [28].”