Shimura Varieties and the Mumford-Tate conjecture, part I

Details Shimura Varieties and the Mumford-Tate conjecture, part I Shimura Varieties and the Mumford-Tate conjecture, part I

2001-09-14

arxiv.org/abs/math/0109094v1

Mathematics

Number Theory

complete, up-dated version

Scientific paper

We prove the Mumford-Tate conjecture for those abelian varieties over number fields, whose simple factors of their adjoint Mumford-Tate groups have over $\dbR$ certain (products of) non-compact factors. In particular, we prove this conjecture for the orthogonal case ($B_n$ and $D_n^{\dbR}$ Shimura types). We construct embeddings of Shimura varieties of (whose adjoints are of prescribed abelian type) into unitary Shimura varieties. We also prove two general theorems involving Frobenius tori of abelian varieties over number fields.

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