About: Mumford–Tate group

In algebraic geometry, the Mumford–Tate group (or Hodge group) MT(F) constructed from a Hodge structure F is a certain algebraic group G. When F is given by a rational representation of an algebraic torus, the definition of G is as the Zariski closure of the image in the representation of the circle group, over the rational numbers. Mumford introduced Mumford–Tate groups over the complex numbers under the name of Hodge groups. introduced the p-adic analogue of Mumford's construction for Hodge–Tate modules, using the work of Tate on p-divisible groups, and named them Mumford–Tate groups.