Some cases of the Mumford-Tate conjecture and Shimura varieties

Adrian Vasiu
2008 Indiana University Mathematics Journal  
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 B_n and D_n^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
more » ... ructions implicitly classify the adjoints of Shimura varieties of PEL type.
doi:10.1512/iumj.2008.57.3513 fatcat:226ochjr7nakjmek273ia7jfwm