Some cases of the Mumford--Tate conjecture and Shimura varieties

Details Some cases of the Mumford--Tate conjecture and Shimura varieties Some cases of the Mumford--Tate conjecture and Shimura varieties

2002-12-04

arxiv.org/abs/math/0212066v7

Indiana Univ. Math. J. 57 (2008), no. 1, pp. 1--75

Mathematics

Number Theory

65 pages. Final version, to appear in Indiana Univ. Math. J

Scientific paper

10.1512/iumj.2008.57.3513

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 constructions implicitly classify the adjoints of Shimura varieties of PEL type.

Affiliated with

Also associated with

No associations

Rating

Some cases of the Mumford--Tate conjecture and Shimura varieties does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Some cases of the Mumford--Tate conjecture and Shimura varieties, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Some cases of the Mumford--Tate conjecture and Shimura varieties will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-265018