4,106 research outputs found
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
of the moduli space such that any point in 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 -divisible groups and their isogeny classes arising from the
abelian varieties in question.Comment: Revised version, 14 page
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