Lecture----数学院晨兴数学中心

Title:	Cycles in the de Rham cohomology of abelian varieties over number fields
Speaker:	Dr. Yunqing Tang ()
Time:	2015-6-16, 15:30-16:30
Place:	N817
Abstract:	In his 1982 paper, Ogus defined a class of cycles in the de Rham cohomology of smooth proper varieties over number fields. In the case of abelian varieties, this class includes all the Hodge cycles by the work of Deligne, Ogus and Blasius, and Ogus predicted that all such cycles are Hodge. I confirm Ogus' prediction for some families of abelian varieties under the assumption that the cycles lie in the Betti cohomology with real coefficients. These families include abelian varieties that have prime dimension and nontrivial endomorphism ring. The proof is based on a theorem of Bost and the known cases of the Mumford--Tate conjecture.
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