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, Ogus predicted that all such cycles are Hodge. In this talk, I will first introduce Ogus’ conjecture as a crystalline analogue of Mumford–Tate conjecture and explain how a theorem of Bost (using transcendence methods à la Chudnovsky) on algebraic foliation is related. In the end, I will discuss the conjecture from the point of view of speical subvarieties of Hodge type Shimura varieties.