Endomorphism algebras of QM abelian surfaces

We determine endomorphism algebras of abelian surfaces with quaternion multiplication.Comment: 14 pages. Lemma 2.10 correcte

A note on the Mumford-Tate Conjecture for CM abelian varieties

The Mumford-Tate conjecture is first proved for CM abelian varieties by H. Pohlmann [Ann. Math., 1968]. In this note we give another proof of this result and extend it to CM motives.Comment: 10 pages, to appear in Taiwanese J. Mat

On the slope stratification of certain Shimura varieties

In this paper we study the slope stratification on the good reduction of the type C family Shimura varieties. We show that there is an open dense subset $U$ of the moduli space such that any point in $U$ can be deformed to a point with a given lower {\it admissible} Newton polygon. For the Siegel moduli spaces, this is obtained by F. Oort which plays an important role in his proof of the strong Grothendieck conjecture concerning the slope stratification. We also investigate the $p$-divisible groups and their isogeny classes arising from the abelian varieties in question.Comment: Revised version, 14 page